influence of the loss of time constants repertoire in pathologic heartbeat dynamics abstract we present a fractal analysis of diurnal heart interbeat time series from healthy young subjects and patients with congestive heart failure we describe some differences between these groups by means of the calculation of some scale invariant exponents a previous simple model to reproduce the observed differences is briefly described phys rev e 67 2003 052901 the model is based in first order autoregressive processes and consists in the combination of time constants we suggest that some changes occurring with disease could be related to the participation or absence of time constants finally we also present a multifractal analysis of simulated sequences and their comparison with real data

the maximal operator on generalized orlicz spaces abstract in this note i present a sufficient condition for the boundedness of the maximal operator on generalized orlicz spaces the result includes as special cases the optimal condition for orlicz spaces as well as the essentially optimal conditions for variable exponent lebesgue spaces and the double phase functional

on some anisotropic reaction diffusion systems with l1 data modeling the propagation of an epidemic disease in this paper we prove the existence of weak solutions for a reaction di usion system with general anisotropic di usivities and transport e ects supplemented with either mixed boundary conditions or no 5ux boundary conditions initial conditions and external forcing terms are in l 1 this does not allow us to use classical variational formulations our motivation is a mathematical model describing the spatial propagation in heterogeneous environments of feline immunode7ciency virus a feline retrovirus 2003 elsevier science ltd all rights reserved msc 35k57 35k55 92d30

a pocket guide to nonlinear differential equations in musielak orlicz spaces abstract the musielak orlicz setting unifies variable exponent orlicz weighted sobolev and double phase spaces they inherit technical difficulties resulting from general growth and inhomogeneity in this survey we present an overview of developments of the theory of existence of pdes in the setting including reflexive and non reflexive cases as well as isotropic and anisotropic ones particular attention is paid to problems with data below natural duality in absence of lavrentiev s phenomenon

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

renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and l1 data abstract in this paper we prove the existence and uniqueness of both renormalized solutions and entropy solutions for nonlinear parabolic equations with variable exponents and l 1 data and moreover we obtain the equivalence of renormalized solutions and entropy solutions

regularity for double phase variational problems we prove sharp regularity theorems for minimisers of a class of variational integrals whose integrand switches between two different types of degenerate elliptic phases according to the zero set of a modulating coefficient a cdot the model case is given by the functional w mapsto int dw p a x dw q rm d x where q p and a cdot geqq 0

nonlinear parabolic equations with measure data in this paper we give summability results for the gradients of solutions of nonlinear parabolic equations whose model isu div u p 2 u on 0 t p with homogeneous cauchy dirichlet boundary conditions wherep 1 and is a bounded measure on 0 t we also study how the summability of the gradient improves if the measure is a function inlm 0 t withm small moreover we give a new proof of the existence of a solution for problem p

steady flow of non newtonian fluids monotonicity methods in generalized orlicz spaces abstract our purpose is to show the existence of weak solutions to steady flow of non newtonian incompressible fluids with nonstandard growth conditions of the cauchy stress tensor we are motivated by the fluids of strongly inhomogeneous behavior and characterized by rapid shear thickening since l p framework is not sufficient to capture the described model we describe the growth conditions with the help of a general x dependent convex function and formulate our problem in generalized orlicz spaces

nonlinear elliptic systems with general growth we prove local lipschitz continuity and as a consequence c k and c regularity of weak solutions u for a class of nonlinear elliptic differential systems of the formn 1 xi a i du 0 1 2 m the growth conditions on the dependence of functions a i on the gradient du are so mild to allow us to embrace growths between the linear and the exponential cases and they are more general than those known in the literature

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

positive solutions of the p x laplace equation with singular nonlinearity abstract in this paper using sub supersolution method we study the positive solution of the p x laplacian equations p x u f x u with dirichlet boundary condition on a bounded domain in r n with c 1 boundary for some 0 1 for a possibly singular nonlinearity f on 0

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms the authors study the nonlinear elliptic equation div a x u du div u g x u f x in with the boundary condition u 0 on where is a bounded open subset of rn a u div a x u du is a nonlinear operator of leray lions type from w1 p0 into its dual c0 r n g x t t 0 and f w 1 p no growth hypothesis is assumed on the vector valued function u the term div u may be meaningless for usual weak solutions even as a distribution the authors deal with a weaker form of solutions of which in w1 p0 are called the renormalized solutions of the original problem this weaker form can be formally obtained from by means of pointwise multiplication by h u where h is a c1 function with compact support they prove the existence of renormalized solutions of and give sufficient conditions under which a renormalized solution is a usual weak solution furthermore the authors study ls and l regularity of renormalized solutions

generalized orlicz spaces and related pde abstract we prove the boundedness of the maximal operator in generalized orlicz spaces defined on subsets of r n the proof is based on an extension result for functions we study generalized sobolev orlicz spaces and establish density of smooth functions and the poincare inequality as applications we establish the existence of solutions of the laplace equation with zero and non zero right hand side further we systematize assumptions for functions and prove several basic tools needed for the study of differential equations of generalized orlicz growth

existence and uniqueness of renormalized solutions to nonlinear elliptic equations with variable exponents and l1 data abstract we prove the existence and uniqueness of a renormalized solution to nonlinear elliptic equations with variable exponents and l 1 data the functional setting involves sobolev spaces with variable exponents w 1 p

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

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

renormalized solutions of nonlinear elliptic problems in generalized orlicz spaces abstract we study a general class of nonlinear elliptic problems associated with the differential inclusion x u div a x u f u f where f l 1 the vector field a is monotone in the second variable and satisfies a non standard growth condition described by an x dependent convex function that generalizes both l p x and classical orlicz settings using truncation techniques and a generalized minty method in the functional setting of non reflexive spaces we prove existence of renormalized solutions for general l 1 data under an additional strict monotonicity assumption uniqueness of the renormalized solution is established sufficient conditions are specified which guarantee that the renormalized solution is already a weak solution to the problem

existence and regularity for mixtures of micromagnetic materials a new model for the energy of a mixture of micromagnetic materials is introduced within the context of functions with special bounded variation existence and regularity for the solution of an optimal design problem in micromagnetics are obtained

pseudo monotone mappings in sobolev orlicz spaces and nonlinear boundary value problems on unbounded domains where r is a domain not necessarily bounded in r in the case where the a have at most polynomial growth in u and its derivatives this problem can be studied in the context of the mappings of monotone type from a sobolev space into its conjugate when the functions a even the top order terms do not obey any polynomial growth it is customary to use a sobolev orlicz space rather than a sobolev space although at the cost of some degree of complexity in the arguments caused mainly by the fact that orlicz spaces are not reflexive in general we shall be dealing here with the latter case the concept of a pseudo monotone operator was introduced to take into account the difference of the properties of the highest order functions a in their top order variables from the lower order derivatives when the domain r is bounded and a polynomial growth condition is satisfied it is a classical result to derive the pseudo monotonicity of the mapping t induced by the operator a in a natural manner from a relatively simple set of hypotheses leray lions conditions on the functions a 3 131 an analogous conclusion for the case of sobolev orlicz spaces was also shown to be true 161 for unbounded domains r other methods were developed to obtain some

sharp regularity for functionals with p q growth we prove regularity theorems for minimizers of integral functionals of the calculus of variations f x du x dx with non standard growth conditions of p q type z p f x z l z q 1 p q in particular we find that a sufficient condition for minimizers to be regular is qp n n where the function f x z is holder continuous with respect to the x variable and x rn this condition is also sharp we include results in the setting of orlicz spaces moreover we treat certain relaxed functionals too finally we address a problem posed by marcellini in 43 showing a minimizer with an isolated singularity

elliptic inequalities with lower order terms and l1 data in orlicz spaces abstract we prove an existence result for solutions of nonlinear elliptic unilateral problems having natural growth terms and l 1 data in orlicz sobolev spaces

entire solutions of multivalued nonlinear schrodinger equations in sobolev spaces with variable exponent abstract we establish the existence of an entire solution for a class of stationary schrodinger equations with subcritical discontinuous nonlinearity and lower bounded potential that blows up at infinity the abstract framework is related to lebesgue sobolev spaces with variable exponent the proof is based on the critical point theory in the sense of clarke and we apply chang s version of the mountain pass lemma without the palais smale condition for locally lipschitz functionals our result generalizes in a nonsmooth framework a result of rabinowitz p h rabinowitz on a class of nonlinear schrodinger equations z angew math phys zamp 43 1992 270 291 on the existence of ground state solutions of the nonlinear schrodinger equation

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

strongly nonlinear parabolic equations with natural growth terms in orlicz spaces abstract we prove approximation and compactness results in inhomogeneous orlicz sobolev spaces and look at as an application the cauchy dirichlet equation u a u g x t u u f w 1 x e m where a is a leray lions operator having a growth not necessarily of polynomial type we also give a trace result allowing to deduce the continuity of the solutions with respect to time

existence of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

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

gradient regularity for quasilinear elliptic dirichlet problems in the plane abstract the problem is addressed of the maximal integrability of the gradient of solutions to quasilinear elliptic equations with merely measurable coefficients in two variables optimal results are obtained in the framework of orlicz spaces and in the more general setting of all rearrangement invariant spaces applications to special instances are exhibited which provide new gradient bounds or improve certain results available in the literature

variational inequalities in orlicz sobolev spaces on etudie l existence de solutions d inegalites variationnelles associees a des operateurs differentiels elliptiques

existence of entire solutions for a class of variable exponent elliptic equations abstract the paper deals with the existence of entire solutions for a quasilinear equation e in r n depending on a real parameter which involves a general variable exponent elliptic operator a in divergence form and two main nonlinearities the competing nonlinear terms combine each other under some conditions we prove the existence of a critical value 0 with the property that e admits nontrivial nonnegative entire solutions if and only if furthermore under the further assumption that the potential a of a is uniform convex we give the existence of a second independent nontrivial nonnegative entire solution of e when our results extend the previous work of autuori and pucci 2013 6 from the case of constant exponents p q and r to the case of variable exponents more interesting we weaken the condition max 2 p q min r p to the simple request that 1 q r furthermore we extend the previous work of alama and tarantello 1996 2 from dirichlet laplacian problems in bounded domains of r n to the case of a general variable exponent differential equation in the entire r n and also remove the assumption q 2 hence the results of this paper are new even in the canonical case p 2

corrigendum to renormalized solutions of nonlinear elliptic problems in generalized orlicz spaces j differential equations 253 2 2012 635 666

renormalized solutions to nonlinear parabolic problems in generalized musielak orlicz spaces abstract we will present the proof of existence of renormalized solutions to a nonlinear parabolic problem t u div a d u f with right hand side f and initial data u 0 in l 1 the growth and coercivity conditions on the monotone vector field a are prescribed by a generalized n function m which is anisotropic and inhomogeneous with respect to the space variable in particular m does not have to satisfy an upper growth bound described by a 2 condition therefore we work with generalized musielak orlicz spaces which are not necessarily reflexive moreover we provide a weak sequential stability result for a more general problem t u div a d u f u f where is a monotone function with respect to the second variable and f is locally lipschitz continuous within the proof we use truncation methods young measure techniques the integration by parts formula and monotonicity arguments which have been adapted to nonreflexive musielak orlicz spaces

necessary and sufficient conditions for absolute continuity of elliptic harmonic measure our purpose in this paper is to give a necessary and sufficient condition on the modulus of continuity of the coefficients of an elliptic operator in divergence form in order that the corresponding poisson kernel for the dirichlet problem exist this condition on the coefficients is global continuity together with the additional property that the modulus of continuity along some nontangential direction at each boundary point be bounded uniformly in these points and directions by a function 7 t satisfying the dini type condition

renormalized solutions for a nonlinear parabolic equation with variable exponents and l 1 data abstract we prove the well posedness existence and uniqueness of a renormalized solution to nonlinear parabolic equations with variable exponents and l 1 data the functional setting involves lebesgue sobolev spaces with variable exponents

some conditions on zeros to avoid step response extrema this note deals with the problem of extrema which may occur in the step response of a linear system with stable real zeros and poles the author gives a simple sufficient condition to avoid extrema using the pole zero configuration of the corresponding transfer function

bounded minimisers of double phase variational integrals bounded minimisers of the functional w mapsto int dw p a x dw q rm d x where 0 leqq a cdot in c 0 alpha and 1 p q are c 1 beta regular provided the sharp bound q leqq p alpha holds

on the cauchy problem for boltzmann equations global existence and weak stability we study the large data cauchy problem for boltzmann equations with general collision kernels we prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in l to a solution from this stability result we deduce global existence of a solution to the cauchy problem our method relies upon recent compactness results for velocity averages a new formulation of the boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions it allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations

overview of differential equations with non standard growth abstract differential equations with non standard growth have been a very active field of investigation in recent years in this survey we present an overview of the field as well as several of the most important results we consider both existence and regularity questions finally we provide a comprehensive list of papers published to date

orlicz sobolev boundary trace embeddings we prove a sharp trace embedding theorem for orlicz sobolev spaces into orlicz spaces on the boundary an optimal trace embedding into more general rearrangement invariant spaces on the boundary is also established

dirichlet problems for fully anisotropic elliptic equations the existence of a non trivial bounded solution to the dirichlet problem is established for a class of nonlinear elliptic equations involving a fully anisotropic partial differential operator the relevant operator depends on the gradient of the unknown through the differential of a general convex function this function need not be radial nor have a polynomial type growth besides providing genuinely new conclusions our result recovers and embraces in a unified framework several contributions in the existing literature and augments them in various special instances

liouville theorems for anisotropic quasilinear inequalities abstract the purpose of this paper is to prove some nonexistence results for nonnegative weak solutions of differential inequalities l u u q or l u u q or l u 0 on r n here l is a quasilinear operator belonging to a wide class of operators including the anisotropic pseudo m laplacian operator the m laplacian operator the mean curvature operator acting in euclidean setting as well as their counterparts in carnot groups setting

differential equations of divergence form in musielak sobolev spaces and a sub supersolution method abstract we study some properties of differential operators of divergence form in musielak sobolev spaces and establish a sub supersolution method for differential equations of divergence form with homogeneous neumann or dirichlet boundary condition in musielak sobolev spaces