Related papers: Gradient estimates for problems with Orlicz growth
We deal with homogeneous Dirichlet and Neumann boundary-value problems for anisotropic elliptic operators of p-Laplace type. They emerge as Euler-Lagrange equations of integral functionals of the Calculus of Variations built upon possibly…
We study the growth of degrees in many autonomous and non-autonomous lattice equations defined by quad rules with corner boundary values, some of which are known to be integrable by other characterisations. Subject to an enabling…
In this paper, we prove sharp estimates and existence results for anisotropic nonlinear elliptic problems with lower order terms depending on the gradient. Our prototype is: $ \left\{ \begin{array}{ll} -\mathcal Q_{p}u =[H(Du)]^{q}+f(x)…
In this paper, the existence, uniqueness and regularity properties, Strichartz type estimates for solution of multipoint Cauchy problem for linear and nonlinear Schr\"odinger equations with general elliptic leading part is obtained.
We study supersolutions and superharmonic functions related to problems involving nonlocal operators with Orlicz growth, which are crucial tools for the development of nonlocal nonlinear potential theory. We provide several fine properties…
We establish interior $W^{2,\delta}$ type estimates for a class of degenerate fully nonlinear elliptic equations with $L^n$ data. The main idea of our approach is to slide $C^{1,\alpha}$ cones, instead of paraboloids, vertically to touch…
For a class of semi-linear elliptic equations with critical Sobolev exponents and boundary conditions, we prove point-wise estimates for blowup solutions and energy estimates. A special case of this class of equations is a locally defined…
Let $n\ge2$ and $\Omega$ be a bounded Lipschitz domain in $\mathbb{R}^n$. In this article, the authors investigate global (weighted) estimates for the gradient of solutions to Robin boundary value problems of second order elliptic equations…
In this paper, firstly, we study gradient estimates for positive solution of the following equation \begin{equation*} \Delta_\xi(u)-\partial_t u- q u =A(u),t\in (-\infty,\infty) \end{equation*} on metric measure space $…
We present some results concerning the solvability of linear elliptic equations in bounded domains with the main coefficients almost in VMO, the drift and the free terms in Morrey classes containing $L_{d}$, and bounded zeroth order…
Second-order two-scale expansions, a unified proof for the regularity of the correctors based on the translation invariant and a lemma for extracting $O(\epsilon)$ from the remainder term are presented for the second order nonlinear…
We consider nonlinear parabolic equations of the type $$ u_t - div a(x, t, Du)= f(x,t) on \Omega_T = \Omega\times (-T,0), $$ under standard growth conditions on $a$, with $f$ only assumed to be integrable. We prove general decay estimates…
In this paper, we study the following nonlocal problem in fractional Orlicz Sobolev spaces \begin{eqnarray*} (-\Delta_{\Phi})^{s}u+V(x)a(|u|)u=f(x,u),\quad x\in\mathbb{R}^N, \end{eqnarray*} where $(-\Delta_{\Phi})^{s}(s\in(0, 1))$ denotes…
Orlicz spaces are generalizations of Lebesgue spaces. The sufficient and necessary conditions for generalized H\"{o}lder's inequality in Lebesgue spaces and in weak Lebesgue spaces are well known. The aim of this paper is to present…
In this manuscript we present an approach to analyze the discontinuous Galerkin solution for general quasilinear elliptic problems. This approach is sufficiently general to extend most of the well-known discretization schemes, including…
In this note we study the global regularity in the Morrey spaces for the second derivatives for the strong solutions of non variational elliptic equations.
The goal of this paper is to study some possibly degenerate elliptic equation in a bounded domain with a nonlinear boundary condition involving measure data. We investigate two types of problems: the first one deals with the laplacian in a…
In this paper we develop numerical analysis for finite element discretization of semilinear elliptic equations with potentially non-Lipschitz nonlinearites. The nonlinearity is essecially assumed to be continuous and monotonically…
We study nonlinear parabolic PDEs with Orlicz-type growth conditions. The main result gives the existence of a unique solution to the obstacle problem related to these equations. To achieve this we show the boundedness of weak solutions and…
In this paper, we prove the existence of solutions to quasilinear elliptic equations on a bounded domain of $\R^N$ under subcritical Musielak-Orlicz-Sobolev growth. Our proofs rely essentially on Mountain Pass Theorem with corresponding…