gradient weighted estimates at the natural exponent for quasilinear parabolic equations abstract in this paper we obtain weighted norm inequalities for the spatial gradients of weak solutions to quasilinear parabolic equations with weights in the muckenhoupt class a q p r n 1 for q p on non smooth domains here the quasilinear nonlinearity is modeled after the standard p laplacian operator until now all the weighted estimates for the gradient were obtained only for exponents q p the results for exponents q p used the full complicated machinery of the calderon zygmund theory developed over the past few decades but the constants blow up as q p essentially because the maximal function is not bounded on l 1 in order to prove the weighted estimates for the gradient at the natural exponent i e q p we need to obtain improved a priori estimates below the natural exponent to this end we develop the technique of lipschitz truncation based on 3 25 and obtain significantly improved estimates below the natural exponent along the way we also obtain improved unweighted calderon zygmund type estimates below the natural exponent which is new even for the linear equations

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

irregular time dependent obstacles abstract we study the obstacle problem for the evolutionary p laplace equation when the obstacle is discontinuous and does not have regularity in the time variable two quite different procedures yield the same solution

global calderon zygmund theory for nonlinear elliptic obstacle problems with asymptotically regular nonlinearities abstract we study a nonlinear elliptic problem with an irregular obstacle in a bounded nonsmooth domain when the nonlinearity is merely asymptotically regular we find an optimal regularity requirement on the associated nonlinearity and a minimal geometric condition on the boundary to ensure a global calderon zygmund estimate for such an asymptotically regular obstacle problem we assume that the associated nonlinearity has a small bmo and the boundary is sufficiently flat in the reifenberg sense

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

calderon zygmund estimates and non uniformly elliptic operators abstract we consider a class of non uniformly nonlinear elliptic equations whose model is given by div d u p 2 d u a x d u q 2 d u div f p 2 f a x f q 2 f where p q and a x 0 and establish the related nonlinear calderon zygmund theory in particular we provide sharp conditions under which the natural and optimal calderon zygmund type result f p a x f q l loc d u p a x d u q l loc holds for every 1 these problems naturally emerge as euler lagrange equations of some variational integrals introduced and studied by marcellini 41 and zhikov 53 in the framework of homogenisation and lavrentiev phenomenon

nonlinear gradient estimates for parabolic problems with irregular obstacles abstract we establish the natural calderon zygmund theory for solutions to parabolic variational inequalities satisfying an irregular obstacle constraint and involving degenerate singular operators in divergence form of general type and proving that the spatial gradient of solutions is as integrable as both the spatial gradient of the obstacles and the inhomogeneous terms under the assumption that the involved nonlinearities have small a bmo semi norm in the spatial variables while they are allowed to be merely measurable in the time variable

global weighted lorentz estimates to nonlinear parabolic equations over nonsmooth domains abstract an elaborate method is developed to establish a global calderon zygmund type theory in weighted lorentz spaces l q t for zero cauchy dirichlet problem of nonlinear parabolic equations of p laplacian type with p 2 d d 2 here we assume that the nonlinearity a a t x is merely measurable in the time variable t and has a mall bmo semi norm in the spatial variables x uniformly in variables while the boundary of bounded domain is flat in the sense of reifenberg our result not only develops nonlinear calderon zygmund theory under weak regularity assumptions on the datum but also extends the related framework from lebesgue spaces to refined weighted lorentz spaces

on the operator l f f log f abstract the present note deals with the operator l h 1 r n d r n which takes a given element f of the hardy space to the function f log f in general this function need not be locally integrable nevertheless due to peculiar cancellations of large positive and negative terms in the integral f log f with c 0 r n we are able to give meaning to f log f as a schwartz distribution we find several alternatives for this interpretation of f log f

elliptic equations with measurable coefficients in reifenberg domains abstract we prove w 1 p estimates for elliptic equations in divergence form under the assumption that for each point and for each sufficiently small scale there is a coordinate system so that the coefficients have small oscillation in n 1 directions we assume the boundary to be reifenberg flat and the coefficients having small oscillation in the flat direction of the boundary

regularity results for a class of functionals with non standard growth we consider the integral functional under non standard growth assumptions that we call p x type namely we assume that a relevant model case being the functional under sharp assumptions on the continuous function p x 1 we prove regularity of minimizers energies exhibiting this growth appear in several models from mathematical physics

global weighted estimates for quasilinear elliptic equations with non standard growth abstract in this paper we obtain a new global gradient estimates in weighted lorentz spaces for weak solutions of p x laplacian type equation with small bmo coefficients in a reifenberg flat domain the modified vitali covering lemma the maximal function technique and the appropriate localization method are the main analytical tools our results improve the known results for such equations

a weighted combining algorithm for spatial multiplexing mimo df relaying systems jointly detecting the signals from the source and relay in a spatial multiplexing sm multiple input multiple output mimo relaying system improves the transmit reliability significantly however the existing joint detection schemes for sm mimo relaying systems which achieve full diversity such as the near maximum likelihood ml decoder suffer from high complexity in this paper we propose a weighted combining wc algorithm which is applied before the detector in the sm mimo decode and forward relaying system the proposed algorithm merges the received signal vectors from the source and relay into a combined signal without expanding their dimension and formulates an equivalent mimo channel matrix for the combined signal resulting in a lower complexity for the subsequent detection we analyze the performance of the proposed wc algorithm with ml detection in terms of the diversity order and computational complexity an approximate upper bound on the symbol error probability sep for the proposed algorithm is also derived simulation results show that in symmetric networks the proposed wc algorithm achieves substantially lower complexity while maintaining an sep performance similar to that of the benchmark nml decoder the consistency of the derived upper bound on the sep is also verified by simulations

regularity results for nonlinear parabolic obstacle problems with subquadratic growth abstract in 26 it was shown that the spatial gradient of the solution u to the parabolic obstacle problem with superquadratic growth is local holder continuous provided the obstacle is regular enough in this paper we extend this regularity result to the subquadratic case this means we establish the local holder continuity of the spatial gradient of the solution u to the parabolic obstacle problem with subquadratic growth more precisely we prove that d u c loc 0 2 for some 0 1 provided the coefficients and the obstacle are regular enough moreover we use the local holder continuity to prove the local lipschitz continuity of the solution u i e u c loc 0 1 1 2

weighted orlicz estimates for general nonlinear parabolic equations over nonsmooth domains we introduce a parabolic analogue of muckenhoupt weights to study optimal weighted regularity in orlicz spaces for a general nonlinear parabolic problem of p laplacian type in divergence form over a nonsmooth domain assuming that the nonlinearity is measurable with respect to the time variable and has a small bounded mean oscillation bmo with respect to the spatial variables that the lateral boundary of the parabolic cylinder is reifenberg flat and that the associated weight belongs to a suitable parabolic muckenhoupt class we obtain a global gradient estimate for such a nonlinear parabolic problem by essentially proving that the gradient of the weak solution is as globally integrable as the nonhomogeneous term in the weighted orlicz space our results extend the existing regularity estimates in lebesgue spaces to weighted orlicz spaces

on the sphere decoding algorithm i expected complexity the problem of finding the least squares solution to a system of linear equations where the unknown vector is comprised of integers but the matrix coefficient and given vector are comprised of real numbers arises in many applications communications cryptography gps to name a few the problem is equivalent to finding the closest lattice point to a given point and is known to be np hard in communications applications however the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known therefore in this paper rather than dwell on the worst case complexity of the integer least squares problem we study its expected complexity averaged over the noise and over the lattice for the sphere decoding algorithm of fincke and pohst we find a closed form expression for the expected complexity both for the infinite and finite lattice it is demonstrated in the second part of this paper that for a wide range of signal to noise ratios snrs and numbers of antennas the expected complexity is polynomial in fact often roughly cubic since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial this suggests that maximum likelihood decoding which was hitherto thought to be computationally intractable can in fact be implemented in real time a result with many practical implications

elliptic equations with bmo coefficients in reifenberg domains the inhomogeneous dirichlet problems concerning divergence form elliptic equations are studied optimal regularity requirements on the coefficients and domains for the w1 p theory 1 p are obtained the principal coefficients are supposed to be in the john nirenberg space with small bmo seminorms the domain is a reifenberg domain these conditions for the w1 p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains in fact these domains might have fractal dimensions 2004 wiley periodicals inc

conjoint optimization an exact branch and bound algorithm for the share of choice problem conjoint analysis is a statistical technique used to elicit partworth utilities for product attributes from consumers to aid in the evaluation of market potential for new products the objective of the share of choice problem a common approach to new product design is to find the design that maximizes the number of respondents for whom the new products utility exceeds a specific hurdle reservation utility we present an exact branch and bound algorithm to solve the share of choice problem our empirical results based on several large commercial data sets and simulated data from a controlled experiment suggest that the approach is useful for finding provably optimal solutions to realistically sized problems including cases where partworths contain estimation error

lorentz estimate for nonlinear parabolic obstacle problems with asymptotically regular nonlinearities abstract in this paper we mainly prove an interior lorentz estimate of the spatial gradient of weak solutions to a class of nonlinear parabolic problems with an irregular obstacle in a bounded cylindrical domain when the nonlinearity is merely asymptotically regular we assume that the associated nonlinearity satisfies certain ellipticity and growth conditions and the r vanishing condition here the approach of constructing a regular obstacle problem via poisson s formula is used to establish lorentz estimate for such an asymptotically regular obstacle problem

a new beamforming design for mimo af relaying systems with direct link in this paper we propose a new beamforming technique that maximizes the end to end signal to noise ratio snr for amplify and forward multiple input multiple output cooperative relaying systems with direct link between thesource and the destination instead of conventional schemes resorting to an iterative method such as a gradient ascentalgorithm our scheme provides a simple closed form solution for source relay joint beamformer designs to this end wefirst derive a new expression of the end to end snr for the cooperative relaying systems and its lower bound which isgiven as the harmonic mean of two individual snrs then a new beamforming scheme which adaptively optimizes one of the two snrs depending on the channel condition is proposed in addition we perform a diversity order analysis of the proposed scheme and show that our scheme achieves a full diversity order of relaying systems with direct link it is confirmed by simulation results that the proposed technique obtains almost identical performance to the gradient ascent algorithm with much reduced complexity and our analytical work accurately predicts the numerical results

higher integrability for minimizers of integral functionals with p q growth abstract we prove higher integrability for minimizers u r n of integral functionals f du a x u dx where f satisfies a non standard growth condition of p q type z p f z l 1 z q p

integral operators on the halfspace in generalized lebesgue spaces lp part ii in this paper we generalize a version of the classical calderon zygmund theorem on principle value integrals in generalized lebesgue spaces lp proved in j reine angew math 563 2003 197 220 to kernels which do not satisfy standard estimates on rd 1 this result will be used in part ii of this paper to prove the classical theorem on halfspace estimates of agmon douglis and nirenberg comm pure appl math 12 1959 623 727 for generalized lebesgue spaces lp

universal potential estimates abstract we prove a class of endpoint pointwise estimates for solutions to quasilinear possibly degenerate elliptic equations in terms of linear and nonlinear potentials of wolff type of the source term such estimates allow to bound size and oscillations of solutions and their gradients pointwise and entail in a unified approach virtually all kinds of regularity properties in terms of the given datum and regularity of coefficients in particular local estimates in holder lipschitz morrey and fractional spaces as well as calderon zygmund estimates follow as a corollary in a unified way moreover estimates for fractional derivatives of solutions by mean of suitable linear and nonlinear potentials are also implied the classical wolff potential estimate by kilpelainen mal and trudinger wang as well as recent wolff gradient bounds for solutions to quasilinear equations embed in such a class as endpoint cases

lorentz estimates for degenerate and singular evolutionary systems we prove estimates of calderon zygmund type for evolutionary p laplacian systems in the setting of lorentz spaces we suppose the coefficients of the system to satisfy only a vmo condition with respect to the space variable our results hold true mutatis mutandis also for stationary p laplacian systems

gradient estimates for a class of parabolic systems we establish local calderon zygmund type estimates for a class of parabolic problems whose model is the nonhomogeneous degenerate singular parabolic p laplacian system ut div du p 2du div f p 2f proving that f lqloc du lqloc q p we also treat systems with discontinuous coefficients of vanishing mean oscillation vmo type

low complexity detection scheme for cooperative mimo systems with decode and forward relays in this paper we study low complexity detection schemes for cooperative multiple input multiple output mimo systems with decode and forward df relays in fixed df protocols the error propagation effect that limits the diversity gain can be overcome by using joint maximum likelihood jml detection but its complexity increases exponentially with the number of streams and modulation orders to develop a low complexity detection scheme we first extend the cooperative maximum ratio combining c mrc scheme to mimo relay networks and then investigate the diversity order of the system we show that c mrc achieves full diversity gain for orthogonal space time code but its diversity gain is limited when the deployed space time code is non orthogonal to address this problem we propose an effective detection scheme that is applicable to arbitrary space time codes on the basis of pairwise error probability approximation max log approximation and the chernoff bound we construct an equivalent point to point mimo signal model and then apply tree search detection techniques compared to jml the proposed detection scheme significantly reduces the detection complexity while preserving diversity gain moreover it can be readily extended to complex field network coding systems whose performance is superior to that of galois field network coding systems analysis and simulation results confirm the efficiency of the proposed scheme

gradient estimates for double phase problems with irregular obstacles abstract an irregular obstacle problem with non uniformly elliptic operator in divergence form of p q growth is studied we find an optimal regularity for such a double phase obstacle problem by essentially proving that the gradient of a solution is as integrable as both the gradient of the assigned obstacle function and the associated nonhomogeneous term in the divergence calderon zygmund type estimates are also obtained under minimal regularity requirements of the prescribed data

global lorentz estimates with variable power to linear parabolic integro differential equations abstract we shall establish a global estimate in the framework of the lorentz spaces for variable power of the fractional derivative of solutions to the cauchy dirichlet problems of linear parabolic integro differential equations with smooth coefficients m t x y 1 2 in a bounded domain here we assume that some higher order derivatives of m t x y in y are merely measurable in the time variable t and satisfy uniformly continuous in the spatial variables x the boundaries of domains are c 1 1 and the variable exponents satisfy log holder continuity

global gradient estimates for general nonlinear parabolic equations in nonsmooth domains we establish the natural calderon zygmund theory for a nonlinear parabolic equation of p laplacian type in divergence form 0 1 ut diva du x t div f p 2f in t by essentially proving that 0 2 f p lq t du p lq t for every q 1 the equation under consideration is of general type and not necessarily of variation form the involved nonlinearity a a x t is assumed to have a small bmo semi norm with respect to x t variables and the lateral boundary of the domain is assumed to be reifenberg flat as a consequence we are able to not only relax the known regularity requirements on the nonlinearity for such a regularity theory but also extend local results to a global one in a nonsmooth domain whose boundary has a fractal property we also find an optimal regularity estimate in orlicz sobolev spaces for such nonlinear parabolic problems

gradient estimates below the duality exponent we show sharp local a priori estimates and regularity results for possibly degenerate non linear elliptic problems with data not lying in the natural dual space we provide a precise non linear potential theoretic analog of classical potential theory results due to adams duke math j 42 765 778 1975 and adams and lewis studia math 74 169 182 1982 concerning morrey spaces imbedding regularity properties for this we introduce a technique allowing for a non local representation of solutions via riesz potentials in turn yielding optimal local estimates simultaneously in both rearrangement and non rearrangement invariant function spaces in fact we also derive sharp estimates in lorentz spaces covering borderline cases which remained open for some while

holder estimates for nonlinear degenerate parabolic sytems on etablit des estimations de holder pour le gradient d espace u des solutions locales faibles des systemes paraboliques degeneres on etablit la continuite de holder des solutions non negatives d une equation parabolique degeneree

performance and optimization of network coded cooperative diversity systems in this paper we study network coded cooperative diversity nccd systems comprising multiple sources one relay and one destination where the relay detects the packets received from all sources and performs galois field gf network coding over rm gf 2 m before forwarding a single packet to the destination assuming independent rayleigh fading for all links of the network we derive simple and accurate closed form approximations for the asymptotic symbol and bit error rates of nccd systems the derived error rate expressions are valid for arbitrary numbers of sources arbitrary modulation schemes and arbitrary constellation mappings and provide significant insight into the impact of various system and channel parameters on performance moreover these expressions can be exploited for optimization of the constellation mapping as well as for formulation of various nccd system optimization problems including optimal power allocation relay selection and relay placement

an end point orlicz type estimate for nonlinear elliptic equations abstract we study nonlinear elliptic equations of p laplacian type in divergence form to establish a natural calderon zygmund type theory of an orlicz space type where the lebesgue space is the special case with t t q p f p l 1 q 2 r d u p l 1 q r in the previous results the estimates obtained were strictly above the natural exponents and the function such as t t log 1 t was ruled out for the candidate of but with our approach can be selected up to the end point case of the estimates and the functions t t and t t log 1 t can be additionally selected for

higher integrability for solutions to parabolic problems with irregular obstacles and nonstandard growth abstract the aim of this paper is to derive the self improving property of integrability for the spatial gradient of solutions to degenerate parabolic obstacle problem with irregular obstacles and p x t nonstandard growth more precisely we prove that the spatial gradient of the solution is integrable to a larger power than the natural one determined by the structural assumptions on the involved differential operator

optimizing product line designs efficient methods and comparisons we take advantage of recent advances in optimization methods and computer hardware to identify globally optimal solutions of product line design problems that are too large for complete enumeration we then use this guarantee of global optimality to benchmark the performance of more practical heuristic methods we use two sources of data 1 a conjoint study previously conducted for a real product line design problem and 2 simulated problems of various sizes for both data sources several of the heuristic methods consistently find optimal or near optimal solutions including simulated annealing divide and conquer product swapping and genetic algorithms

weighted and regularity estimates for nonlinear equations on reifenberg flat domains abstract global weighted l p estimates are obtained for the gradient of solutions to nonlinear elliptic dirichlet boundary value problems over a bounded nonsmooth domain morrey and holder regularity of solutions are also established as a consequence these results generalize various existing estimates for nonlinear equations the nonlinearities are of at most linear growth and assumed to have a uniform small mean oscillation the boundary of the domain on the other hand may exhibit roughness but assumed to be sufficiently flat in the sense of reifenberg our approach uses maximal function estimates and vitali covering lemma and also known regularity results of solutions to nonlinear homogeneous equations

optimal product design using conjoint analysis computational complexity and algorithms abstract the problem of maximizing the share of a new product introduced in a competitive market is shown to be np hard a directed graph representation of the problem is used to construct shortest path and dynamic programming heuristics both heuristics are shown to have arbitrarily bad worst case bounds computational experience with real sized problems is reported both heuristics identify near optimal solutions for the simulated problems the dynamic programming heuristic performing better than the shortest path heuristic

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

performance analysis of mmse based amplify and forward spatial multiplexing mimo relaying systems in this paper we propose a general framework to quantify the average error probability of the minimum mean squared error based precoding schemes in amplify and forward relay networks where all nodes are equipped with multiple antennas especially we investigate spatial multiplexing schemes which transmit multiple data streams simultaneously due to difficulty in finding an exact expression of the average error rate we exploit the high signal to noise ratio snr based approach which allows a simple and accurate characterization of the performance then we derive new closed form expressions for bit error rate performance of both the optimal source relay joint precoding schemes and the optimal relay only precoding schemes in terms of a coding gain as well as a diversity gain taking a different pathloss in each hop into consideration we evaluate the performance in a generalized environment through our analysis we discuss several interesting observations and provide a helpful guideline for designing mmse based relaying systems monte carlo simulations show that our analytical work accurately predicts numerical results

on w1 p estimates for elliptic equations in divergence form first we will apply the method to study w 1 p regularity for a nonlinear elliptic operator in divergence form we would like to point out that in the particular case of a linear elliptic equation this method gives an alternative proof to the classical one which uses the general theory of singular integrals the utility of the method that we describe below is that hypotheses a and b are obtained directly by studying the deviation of the coefficients of a from the coefficients of a0 and this is usually not a difficult task a more interesting application of this kind of approximation method is to elliptic homogenization problems for which we obtain results that give w 1 p estimates with a weak hypothesis of regularity in the coefficients for instance we are able to study the following cases

weighted lorentz estimate for asymptotically regular parabolic equations of p x t laplacian type abstract we prove a global weighted lorentz estimate of the spatial gradients of weak solution to the cauchy dirichlet problem for asymptotically regular parabolic equations of p x t laplacian type in a reifenberg flat domain it is mainly assumed that the associated regular nonlinearity is measurable with respect to the time variable and satisfies the r vanishing condition with respect to the spatial variables

variable lorentz estimate for conormal derivative problems of stationary stokes system with partially bmo coefficients abstract we prove a global calderon zygmund type estimate in the framework of lorentz spaces for the variable power of the gradients to the solution pair u p of the conormal derivative problems of stationary stokes system it is mainly assumed that the leading coefficients are merely measurable in one of the spatial variables and have sufficiently small bounded mean oscillation seminorm in the other variables the boundary of domain belongs to the reifenberg flatness and the variable exponents p x satisfy the log holder continuity

lorentz estimates for obstacle parabolic problems we prove that the spatial gradient of variational solutions to parabolic obstacle problems of p laplacian type enjoys the same regularity of the data and of the derivatives of the obstacle in the scale of lorentz spaces

variable lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities abstract we prove global calderon zygmund type estimate in lorentz spaces for variable power of the gradients to weak solution of nonlinear elliptic equations in a non smooth domain we mainly assume that the nonlinearities are merely measurable in one of the spatial variables and have sufficiently small bmo semi norm in the other variables the boundary of domain belongs to reifenberg flatness and the variable exponents p x satisfy log holder continuity

elliptic equations with measurable nonlinearities in nonsmooth domains abstract we study elliptic equations with measurable nonlinearities in nonsmooth domains we establish an optimal global w 1 p estimate under the condition that the associated nonlinearity is allowed to be merely measurable in one variable but has a sufficiently small bmo semi norm in the other variables while the underlying domain is sufficiently flat in the reifenberg sense that the boundary of the domain is locally trapped between two narrow strips

global regularity in lorentz spaces for nonlinear elliptic equations with lp logl growth abstract we prove a global calderon zygmund type estimate in the framework of lorentz spaces for the gradients of weak solutions of nonlinear elliptic equations with l p log l growth more precisely by considering the zero dirichlet problem of the elliptic equation div a x d u div h x f x with a x d a x p x log e for any 0 a x 0 0 and h x f p x 1 log e f we obtain x f l t q x d u l t q for t 1 and q 0 where x p x log e under the assumptions that the function a has a small bounded mean oscillation seminorm p x satisfies strong log holder continuity and the underlying domain is reifenberg flat

an optimization framework for product design an important problem in the product design and development process is to use the part worths preferences of potential customers to design a new product such that market share is maximized the authors present a new optimization framework for this problem the nested partitions np method this method is globally convergent and may utilize existing heuristic methods to speed its convergence we incorporate several known heuristics into this framework and demonstrate through numerical experiments that using the np method results in superior product designs our numerical results suggest that the new framework is particularly useful for designing complex products with many attributes

regularity results for a class of non differentiable obstacle problems abstract in this paper we prove the higher differentiability in the scale of besov spaces of the solutions to a class of obstacle problems of the type min f x z d z z k here is an open bounded set of r n n 2 is a fixed function called obstacle and k is set of admissible functions z w 1 p such that z a e in we assume that the gradient of the obstacle belongs to a suitable besov space the main novelty here is that we are not assuming any differentiability on the partial maps x f x z d z and z f x z d z but only their holder continuity

mappings of bmo bounded distortion this paper can be viewed as a sequel to the work 9 where the theory of mappings of bmo bounded distortion is developed largely in even dimensions using singular integral operators and recent developments in the theory of higher integrability of jacobians in hardy orlicz spaces in this paper we continue this theme refining and extending some of our earlier work as well as obtaining results in new directions the planar case was studied earlier by g david 4 in particular he obtained existence theorems modulus of continuity estimates and bounds on area distortion for mappings of bmo distortion in fact in slightly more generality we obtain similar results in all even dimensions one of our main new results here is the extension of the classical theorem of painleve concerning removable singularties for bounded analytic functions to the class of mappings of bmo bounded distortion the setting of the plane is of particular interest and somewhat more can be said here because of the existence theorem or the measurable riemann mapping theorem which is not available in higher dimensions we give a construction to show our results are qualitatively optimal another surprising fact is that there are domains which support no bounded quasiregular mappings but admit

lorentz estimates to nonlinear elliptic obstacle problems of p x growth in reifenberg domains abstract we prove a global estimate in the scale of lorentz spaces for the gradient of weak solution to a general nonlinear obstacle problem of p x growth it is mainly assumed that the nonlinearity satisfies small bmo semi norm in the spatial variable and the boundary of domain is flat in the reifenberg sense while the variable exponent p x is a strongly log holder continuous function here an essential ingredient of our main proof is to make use of a combination of the so called large m inequality principle and the geometric argument

a branch and price approach to the share of choice product line design problem we develop a branch and price algorithm for constructing an optimal product line using partworth estimates from choice based conjoint analysis the algorithm determines the specific attribute levels for each multiattribute product in a set of products to maximize the resulting product line s share of choice i e the number of respondents for whom at least one new product s utility exceeds the respondent s reservation utility computational results using large commercial and simulated data sets demonstrate that the algorithm can identify provably optimal robust solutions to realistically sized problems

lorentz estimates for fully nonlinear parabolic and elliptic equations abstract we prove an interior lorentz estimate of the hessian of strong solutions to fully nonlinear parabolic equations u t f d 2 u x t f x t and elliptic equations f d 2 u x f x respectively here we assume that the associated nonlinearities satisfy uniformly parabolic condition or ellipticity certain growth condition and the r vanishing condition we establish lorentz estimates for such fully nonlinear equations based on the approach of the large m inequality principle introduced by acerbi mingione

linear potentials in nonlinear potential theory pointwise gradient bounds via riesz potentials such as those available for the linear poisson equation actually hold for general quasilinear degenerate equations of p laplacean type the regularity theory of such equations completely reduces to that of the classical poisson equation up to the c1 level

gradient estimates for the p x laplacean system we prove calderon and zygmund type estimates for a class of elliptic problems whose model is the non homogeneous p x laplacean system div jduj p x 2 du div jf j p x 2 f

gradient estimates for nonlinear elliptic double obstacle problems abstract we study a nonlinear elliptic double obstacle problem with irregular data and establish an optimal calderon zygmund theory the partial differential operator is of the p laplacian type and includes merely measurable coefficients in one variable we prove that the gradient of a weak solution is as integrable as both the gradient of assigned two obstacles and the nonhomogeneous divergence term under a small bmo semi norm assumption on the coefficients in the other variables

lorentz estimate with a variable power for parabolic obstacle problems with non standard growths abstract we prove a global lorentz estimate for the variable power of the gradients of weak solution to parabolic obstacle problems with p t x growth over a bounded nonsmooth domain it is mainly assumed that the variable exponents p t x satisfy a strong type log holder continuity the associated nonlinearities are merely measurable in the time variable and have small bmo semi norms in the spatial variables while the underlying domain is quasiconvex

linear transmit processing in mimo communications systems we examine and compare the different types of linear transmit processing for multiple input multiple output systems where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters we can identify three filter types similar to receive processing the transmit matched filter the transmit zero forcing filter and the transmit wiener filter we show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power moreover the transmit wiener filter has similar convergence properties as the receive wiener filter i e it converges to the matched filter and the zero forcing filter for low and high signal to noise ratio respectively we give closed form solutions for all transmit filters and present the fundamental result that their mean square errors are equal to the errors of the respective receive filters if the information symbols and the additive noise are uncorrelated however our simulations reveal that the bit error ratio results of the transmit filters differ from the results for the respective receive filters

higher order elliptic and parabolic systems with variably partially bmo coefficients in regular and irregular domains abstract the solvability in sobolev spaces is proved for divergence form complex valued higher order parabolic systems in the whole space on a half space and on a reifenberg flat domain the leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder the directions in which the coefficients are only measurable vary depending on each cylinder the corresponding elliptic problem is also considered