covering relations for multidimensional dynamical systems abstract we present a topological technique for analyzing dynamical systems with complex behavior based on the general notion of covering relations our method can be used to study multidimensional dynamical systems with an arbitrary number of topologically expanding directions

variability in production of the vowels i and a a hypothesis on the nature of articulatory targets for the vowels i and a is proposed based on acoustic considerations and vowel articulations the conjecture is that positioning of points on the tongue surface in a repetition experiment should be most accurate in the direction perpendicular to the vocal tract midline at the acoustically critical point of maximal constriction for each vowel the hypothesis was tested by examining x ray microbeam data for three speakers conducting a partial acoustical analysis and performing a modeling study distributions were plotted of the midsagittal locations of three tongue points at the time of maximal excursion toward the vowel target for numbers of examples of the vowels embedded in a variety of phonetic contexts more variation was found along a direction parallel to the vocal tract midline than perpendicular to the midline supporting the hypothesis statistics on formant values for one subject have been calculated and pairwise regressions of displace

sobolev embeddings in metric measure spaces with variable dimension in this article we study metric measure spaces with variable dimension we consider lebesgue spaces on these sets and embeddings of the riesz potential in these spaces we also investigate hajlasz type sobolev spaces and prove sobolev and trudinger inequalities with optimal exponents all of these questions lead naturally to function spaces with variable exponents

probing the independence of formant control using altered auditory feedback two auditory feedback perturbation experiments were conducted to examine the nature of control of the first two formants in vowels in the first experiment talkers heard their auditory feedback with either f1 or f2 shifted in frequency talkers altered production of the perturbed formant by changing its frequency in the opposite direction to the perturbation but did not produce a correlated alteration of the unperturbed formant thus the motor control system is capable of fine grained independent control of f1 and f2 in the second experiment a large meta analysis was conducted on data from talkers who received feedback where both f1 and f2 had been perturbed a moderate correlation was found between individual compensations in f1 and f2 suggesting that the control of f1 and f2 is processed in a common manner at some level while a wide range of individual compensation magnitudes were observed no significant correlations were found between individuals compensations and vowel space differences similarly no significant correlations were found between individuals compensations and variability in normal vowel production further when receiving normal auditory feedback most of the population exhibited no significant correlation between the natural variation in production of f1 and f2

linear degrees of freedom in speech production analysis of cineradio and labio film data and articulatory acoustic modeling the following contribution addresses several issues concerning speech degrees of freedom in french oral vowels stop and fricative consonants based on an analysis of tongue and lip shapes extracted from cineradio and labio films the midsagittal tongue shapes have been submitted to a linear decomposition where some of the loading factors were selected such as jaw and larynx position while four other components were derived from principal component analysis pca for the lips in addition to the more traditional protrusion and opening components a supplementary component was extracted to explain the upward movement of both the upper and lower lips in v production a linear articulatory model was developed the six tongue degrees of freedom were used as the articulatory control parameters of the midsagittal tongue contours and explained 96 of the tongue data variance these control parameters were also used to specify the frontal lip width dimension derived from the labio film front views finally this model was complemented by a conversion model going from the midsagittal to the area function based on a fitting of the midsagittal distances and the formant frequencies for both vowels and consonants

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

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

besov spaces with variable smoothness and integrability abstract in this article we introduce besov spaces with variable smoothness and integrability indices we prove independence of the choice of basis functions as well as several other basic properties we also give sobolev type embeddings and show that our scale contains variable order holder zygmund spaces as special cases we provide an alternative characterization of the besov space using approximations by analytic functions

existence and multiplicity results for a new p x kirchhoff problem abstract in this work we study the existence and multiplicity results for the following nonlocal p x kirchhoff problem 0 1 a b 1 p x u p x d x d i v u p x 2 u u p x 2 u g x u in u 0 on where a b 0 are constants r n is a bounded smooth domain p c with n p x 1 is a real parameter and g is a continuous function the analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties

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

global calderon zygmund estimates for a class of nonlinear elliptic equations with neumann data abstract in this paper we obtain the following global calderon zygmund estimates b f l q b u l q for any q 1 in a convex domain of the weak solution for a class of quasilinear elliptic equations with the neumann data div a u u div a f f in a u u a f f on where b t 0 t a d for t 0 moreover we remark that b t t p log 1 t satisfies the given conditions in this work

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

regularity results for stationary electro rheological fluids we prove regularity results for weak solutions to systems modelling electro rheological fluids in the stationary case as proposed in 27 31 a particular case of the system we consider is

eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent in this paper we are concerned with a new class of anisotropic quasilinear elliptic equations with a power like variable reaction term one of the main features of our work is that the differential operator involves partial derivatives with different variable exponents so that the functional analytic framework relies upon anisotropic sobolev and lebesgue spaces existence and nonexistence results are deeply influenced by the competition between the growth rates of the anisotropic coefficients our main results point out some striking phenomena related to the existence of a continuous spectrum in several distinct situations

harmonic type approximation lemmas we give a survey of known and not known harmonic type approximation lemmas which are descendants of the classical de giorgi s one and we outline some of their recent or possible applications

regularity of solutions to a class of variable exponent fully nonlinear elliptic equations abstract in the present paper we propose the investigation of variable exponent degenerate singular elliptic equations in non divergence form this current endeavor parallels the by now well established theory of functionals satisfying nonstandard growth condition which in particular encompasses problems ruled by the p x laplacian operator under rather general conditions we prove viscosity solutions to variable exponent fully nonlinear elliptic equations are locally of class c 1 for a universal constant 0 1 a key feature of our estimates is that they do not depend on the modulus of continuity of exponent coefficients and thus may be employed to investigate a variety of problems whose ellipticity degenerates and or blows up in a discontinuous fashion

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

lp λ regularity for fully nonlinear elliptic equations abstract we establish the variable exponent morrey spaces l p estimate to the dirichlet problem for fully nonlinear elliptic equations on a c 1 1 bounded domain for variable exponents p and

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

abstract hardy spaces with variable exponents abstract in this paper we introduce the definition of abstract hardy spaces with variable exponents via the atomic decomposition and molecular decomposition we prove the continuity from our variable hardy space h a t o p into l p where p r n 0 1 0 p p 1 moreover we investigate the bilinear theory finally we give an application of the abstract hardy spaces with variable exponents

developments and perspectives in nonlinear potential theory abstract nonlinear potential theory aims at replicating the classical linear potential theory when nonlinear equations are considered in recent years there has been a substantial development of this subject mostly linked to the possibility of proving pointwise estimates for solutions to nonlinear equations via linear and nonlinear potentials here we give a brief account of such developments and outline the connections with different fields

global gradient estimates for the p laplacian abstract we consider calderon zygmund type estimates for the non homogeneous p laplacian system div d u p 2 d u div g p 2 g where p is a variable exponent we show that g p l q r n l 1 r n implies d u p l q r n l 1 r n for any q 1 we also prove local estimates independent of the size of the domain and introduce new techniques to variable analysis the paper is an extension of the local estimates of acerbi mingione 2005

global gradient estimates for the parabolic p x t laplacian equation abstract in this paper we consider the global gradient estimates for weak solutions of the parabolic p x t laplacian type equation in a reifenberg flat domain

the singular set of minima of integral functionals in this paper we provide upper bounds for the hausdorff dimension of the singular set of minima of general variational integrals open image in new window where f is suitably convex with respect to dv and holder continuous with respect to x v in particular we prove that the hausdorff dimension of the singular set is always strictly less than n where open image in new window

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

global regularity for higher order divergence elliptic and parabolic equations abstract in this paper we obtain the global regularity estimates of the weak solutions in sobolev spaces and orlicz spaces for higher order elliptic and parabolic equations of divergence form with small bmo coefficients in the whole space we only focus on the parabolic case while the corresponding result in the elliptic case can be obtained as a corollary

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

lorentz estimates for a class of nonlinear parabolic systems abstract in this paper we obtain the following local lorentz estimates b f l l o c q b u l l o c q for any 1 and 0 q of the weak solutions for a class of quasilinear parabolic systems u t div a u u div a f f where b t 0 t a d for t 0

lipschitz type smoothness of the fractional integral on variable exponent spaces fil ramseyer mauricio javier consejo nacional de investigaciones cientificas y tecnicas centro cientifico tecnologico conicet santa fe instituto de matematica aplicada del litoral universidad nacional del litoral instituto de matematica aplicada del litoral argentina

weak shadowing for discrete dynamical systems on nonsmooth manifolds abstract in j math anal appl 189 1995 409 423 corless and pilyugin proved that weak shadowing is a c 0 generic property in the space of discrete dynamical systems on a compact smooth manifold m in our paper we give another proof of this theorem which does not assume that m has a differential structure moreover our method also works for systems on some compact metric spaces that are not manifolds such as a hilbert cube or generally a countably infinite cartesian product of manifolds with boundary and a cantor set

regularity estimates for nonlinear elliptic measure data problems with nonstandard growth abstract we prove a global calderon zygmund type estimate for the gradient of a solution to a nonlinear elliptic problem with nonstandard growth when the right hand side is a bounded radon measure minimal regularity requirements on both the nonlinearity and the boundary of the domain are investigated for such a gradient estimate

an eigenvalue problem with variable exponents abstract a highly nonlinear eigenvalue problem is studied in a sobolev space with variable exponent the euler lagrange equation for the minimization of a rayleigh quotient of two luxemburg norms is derived the asymptotic case with a variable infinity is treated local uniqueness is proved for the viscosity solutions

local gradient estimates for nonlinear elliptic equations abstract in this paper we obtain local l q q p gradient estimates for weak solutions of elliptic equations of p laplacian type with small bmo coefficients

s limit shadowing is c0 dense abstract we prove see theorem 1 that the set of maps resp surjective maps with the shadowing property is c 0 residual in the space of all continuous maps resp continuous surjective maps of a compact topological manifold possibly with boundary which extends the similar result known for homeomorphisms pilyugin and plamenevskaya 1999 22 as well as generalize the analogous result for maps koscielniak et al preprint 2013 12 obtained under an additional assumption that the manifold admits some kind of a piecewise linear structure moreover we prove see theorem 2 that the set of maps resp surjective maps with the s limit shadowing property is c 0 dense in the space of all continuous maps resp continuous surjective maps

maximum principles for anisotropic elliptic inequalities we establish some maximum and comparison principles for weak distributional solutions of anisotropic elliptic inequalities in divergence form both in the homogeneous and non homogeneous case the main prototypes we have in mind are inequalities involving the p laplace operator and the generalized mean curvature operator

higher integrability for nonlinear elliptic equations with variable growth abstract in this paper based on the theory of variable exponent spaces we study the regularity for a class of nonlinear elliptic equation with p x laplacian under suitable assumptions we obtain a local gradient estimate in the orlicz space for weak solution

perceptuomotor bias in the imitation of steady state vowels previous studies suggest that speakers are systematically inaccurate or biased when imitating self produced vowels the direction of these biases in formant space and their variation may offer clues about the organization of the vowel perceptual space to examine these patterns three male speakers were asked to imitate 45 self produced vowels that were systematically distributed in f1 f2 space all three speakers showed imitation bias and the bias magnitudes were significantly larger than those predicted by a model of articulatory noise each speaker showed a different pattern of bias directions but the pattern was unrelated to the locations of prototypical vowels produced by that speaker however there were substantial quantitative regularities 1 the distribution of imitation variability and bias magnitudes were similar for all speakers 2 the imitation variability was independent of the bias magnitudes and 3 the imitation variability a production measure was commensurate with the formant discrimination limen a perceptual measure these results indicate that there is additive gaussian noise in the imitation process that independently affects each formant and that there are speaker dependent and potentially nonlinguistic biases in vowel perception and production

higher integrability for a quasilinear parabolic equation of p laplacian type abstract in this paper we generalize classical l q q p estimates of the gradient to the orlicz space for weak solutions of a quasilinear parabolic equation of p laplacian type

on genericity of shadowing and periodic shadowing property abstract let m be a smooth compact manifold possibly with boundary or compact manifold with dim m 3 or dim m 6 we prove that generic homeomorphism on m has the periodic shadowing property

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

interior a priori estimates for solutions of fully non linear equations on etend une theorie de perturbations aux solutions d equations uniformement elliptiques d ordre 2 totalement non lineaires

on the periodic orbits shadowing and strong transitivity of continuous flows abstract we prove that chaotic flows i e flows that satisfy the shadowing property and have a dense subset of periodic orbits satisfy a reparametrized gluing orbit property similar to the one introduced in bomfim and varandas 2015 in particular these are strongly transitive in balls of uniform radius we also prove that the shadowing property for a flow and a generic time t map and having a dense subset of periodic orbits hold for a c 0 baire generic subset of lipschitz vector fields that generate continuous flows similar results also hold for c 0 generic homeomorphisms and in particular we deduce that chain recurrent classes of c 0 generic homeomorphisms have the gluing orbit property

local calderon zygmund estimates for parabolic minimizers abstract we establish local calderon zygmund estimates for parabolic minimizers u to certain variational inequalities the formal corresponding parabolic partial differential equation would be t u div f z u d u u f z u d u div f p 2 f h with p 2 n n 2 however since we do not impose any condition on the existence of the derivative u f the pde above may not have any meaning at all for proving the calderon zygmund estimates we thus remain solely on the level of parabolic minimizers precisely for q p we prove that d u l loc q if u is locally holder continuous and f l loc q and h l loc q for a q depending on q

riesz potential estimates for a class of double phase problems abstract a double phase problem with a bounded borel measure on the right hand side is studied we prove an optimal pointwise gradient estimate for such a measure data problem via riesz potentials of the measure under log dini continuity assumption on the modulating coefficients as a consequence we find an optimized c 1 regularity criterion

boundary regularity in variational problems we prove that if u omega subset mathbb r n to mathbb r n is a solution to the dirichlet variational problem mathop rm min limits w int omega f x w dw rm d x quad rm subject to quad w equiv u 0 rm on partial omega involving a regular boundary datum u 0 and a regular integrand f x w dw strongly convex in dw and satisfying suitable growth conditions then mathcal h n 1 almost every boundary point is regular for u in the sense that du is holder continuous in a relative neighborhood of the point the existence of even one such regular boundary point was previously not known except for some very special cases treated by jost meier math ann 262 549 561 1983 our results are consequences of new up to the boundary higher differentiability results that we establish for minima of the functionals in question the methods also allow us to improve the known boundary regularity results for solutions to non linear elliptic systems and in some cases to improve the known interior singular sets estimates for minimizers moreover our approach allows for a treatment of systems and functionals with rough coefficients belonging to suitable sobolev spaces of fractional order

parabolic equations in reifenberg domains natural sobolev type estimates are proved for weak solutions of inhomogeneous parabolic equations in divergence form in a bounded cylinder 0 t which is reifenberg flat in the space direction the principal coefficients of the operator are assumed to be in bmo space with their bmo semi norms small enough

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