Variational inequalities in Musielak-Orlicz-Sobolev spaces

M. Sidi El Vally, Abdelmoujib Benkirane

Publication date: 26 February 2015

Published in: Bulletin of the Belgian Mathematical Society - Simon Stevin (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bbms/1420071854

zbMATH Keywords

variational inequalities obstacle problem elliptic boundary value problem Musielak-Orlicz-Sobolev spaces strongly nonlinear problem the trace mapping

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Boundary value problems for first-order elliptic systems (35J56) Quasilinear elliptic equations (35J62)

Related Items (61)

On double-phase problems without any growth and Ambrosetti–Rabinowitz conditions ⋮ Ground state sign-changing solutions for a class of double-phase problem in bounded domains ⋮ Infinitely many positive solutions for a double phase problem ⋮ Existence of renomalized solution for nonlinear elliptic boundary value problem without \(\Delta_2\)-condition ⋮ Existence result for nonlinear elliptic unilateral problems in Musielak framework with \(L^1\) data ⋮ Gradient estimates for double phase problems with irregular obstacles ⋮ Existence of solutions to parabolic equation with \(L^1\) data in Musielak spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Strongly nonlinear elliptic boundary value problems in Musielak-Orlicz spaces ⋮ Existence of solutions for double-phase problems by topological degree ⋮ Nonlinear unilateral parabolic problems in Musielak-Orlicz spaces with \(L^1\) data ⋮ Nonlinear unilateral problems without sign condition in Musielak spaces ⋮ Strongly nonlinear elliptic problem with measure data in Musielak-Orlicz spaces ⋮ Correction to: ``Elliptic inequalities with \(L^1\) data in Musielak-Orlicz spaces ⋮ Existence result of entropy solution for some nonlinear parabolic problems under natural growths in Musielak spaces ⋮ On solutions of nonlinear elliptic equations with \(L_1\)-data in unbounded domains ⋮ Unnamed Item ⋮ Renormalized non-negative solutions for the double phase Dirichlet problems with L1 data ⋮ Existence of solutions for a class of nonlinear elliptic problems with measure data in the setting of Musielak-Orlicz-Sobolev spaces ⋮ Numerical analysis of a nonlinear discrete duality finite volume scheme for Leray-Lions type elliptic problems in Orlicz spaces ⋮ Some properties of Musielak spaces with only the log-Hölder continuity condition and application ⋮ Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain ⋮ On Some Nonlinear Elliptic Problems with Large Monotonocity in Musielak–Orlicz–Sobolev Spaces ⋮ Some applications of the log-Hölder continuity condition in generalized Musielak-Orlicz spaces ⋮ Infinitely many low- and high-energy solutions for double phase problems with nonstandard growth ⋮ Multiple nontrivial solutions for superlinear double phase problems via Morse theory ⋮ A strongly nonlinear elliptic problem with generalized growth in Musielak spaces ⋮ On some nonlinear obstacle problems with only the log-Hölder continuity in Musielak spaces ⋮ Nonlinear parabolic systems in Musielack-Orlicz space ⋮ The Nehari manifold for double‐phase problems with convex and concave nonlinearities ⋮ Equivalence of entropy and renormalized solutions of a nonlinear elliptic problem in Musielak-Orlicz spaces ⋮ Variational nonlinear elliptic equations in nonreflexive Musielak spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Entropy solutions for parabolic equations in Musielak framework without sign condition and with measure data ⋮ Barrier solutions of elliptic differential equations in Musielak-Orlicz-Sobolev spaces ⋮ Existence of solution for double-phase problem with singular weights ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Global gradient estimates for the borderline case of double phase problems with BMO coefficients in nonsmooth domains ⋮ Global gradient estimates for non-uniformly elliptic equations ⋮ Elliptic inequalities with \(L^1\) data in Musielak-Orlicz spaces ⋮ An existence result of entropy solutions to elliptic problems in generalized Orlicz-Sobolev spaces ⋮ Entropy solutions to parabolic equations in Musielak framework involving non coercivity term in divergence form ⋮ \(L^\infty\)-bounds of solutions for a class of strongly nonlinear elliptic equations in Musielak spaces ⋮ Gradient estimates for multi-phase problems ⋮ Existence of solutions for some nonlinear elliptic problems involving Minty's lemma ⋮ Lagrange Multiplier Rule to a Nonlinear Eigenvalue Problem in Musielak–Orlicz Spaces ⋮ On a class of double-phase problem without Ambrosetti–Rabinowitz-type conditions ⋮ Existence and nonexistence of solutions for the double phase problem ⋮ Existence of solutions for some nonlinear elliptic equations in Musielak spaces with only the log-Hölder continuity condition ⋮ Elliptic inequalities with lower-order terms and \(L^1\) data in Musielak-Orlicz spaces ⋮ Renormalized solution for a nonlinear parabolic problems with noncoercivity in divergence form in Musielak-Orlicz spaces ⋮ On a double phase problem with sublinear and superlinear nonlinearities ⋮ Calderón-Zygmund estimates for generalized double phase problems ⋮ Equivalence between distributional and viscosity solutions for the double-phase equation ⋮ Existence of infinitely many solutions for double phase problem with sign-changing potential ⋮ Multiple solutions for a class of double phase problem without the Ambrosetti-Rabinowitz conditions ⋮ Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces

This page was built for publication: Variational inequalities in Musielak-Orlicz-Sobolev spaces