Structural stability for variable exponent elliptic problems. I: The \(p(x)\)-Laplacian kind problems

DOI10.1016/j.na.2010.02.039zbMath1191.35126OpenAlexW1995657843MaRDI QIDQ975236

Boris P. Andreianov, Stanislas Ouaro, Mostafa Bendahmane

Publication date: 9 June 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.02.039

zbMATH Keywords

Young measureswell-posednessLeray-Lions operatorvariable exponentcontinuous dependence\(p(x)\)-Laplacianconvergence of minimizersthermorheological fluids

Mathematics Subject Classification ID

Non-Newtonian fluids (76A05) Nonlinear elliptic equations (35J60) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Weak solutions to PDEs (35D30)

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Cites Work

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• Orlicz spaces and modular spaces
• Solvability of the three-dimensional thermistor problem
• Existence and uniqueness of renormalized solutions to nonlinear elliptic equations with variable exponents and \(L^{1}\)-data
• Modeling, mathematical and numerical analysis of electrorheological fluids.
• The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values
• On the existence and stability of solutions for Dirichlet problem with \(p(x)\)-Laplacian
• On stationary thermo-rheological viscous flows
• Nonlinear elliptic and parabolic equations involving measure data
• On passage to the limit in nonlinear elliptic equations
• Steady flow of non-Newtonian fluids - monotonicity methods in generalized Orlicz spaces
• Structural stability for variable exponent elliptic problems. II: The \(p(u)\)-Laplacian and coupled problems
• Existence results for a class of \(p\)-Laplacian problems with sign-changing weight.
• A class of nonlinear elliptic problems
• On a solution of degenerate elliptic-parabolic systems in Orlicz-Sobolev spaces. I, II
• Quasilinear elliptic-parabolic differential equations
• On some variational problems
• Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems
• Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms
• Parametrized measures and variational principles
• A refinement of Ball's theorem on Young measures
• Nonlinear elliptic systems with measure-valued right hand side
• Density \(C_0^{\infty}(\mathbb{R}^n)\) in the generalized Sobolev spaces \(W^{m,p(x)}(\mathbb{R}^n)\).
• Continuous dependence with respect to the operator of entropy solutions of elliptic problems with right hand side in \(L^1\)
• \(L^ 1\)-contraction and uniqueness for quasilinear elliptic-parabolic equations
• Quasi-linear parabolic systems in divergence form with weak monotonicity
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Minimizers of the variable exponent, non-uniformly convex Dirichlet energy
• \(\varGamma \)-convergence and homogenization of functionals in Sobolev spaces with variable exponents
• Existence of solutions for \(p(x)\)-Laplacian problems on a bounded domain
• Renormalized solutions for nonlinear elliptic equations with variable exponents and \(L^1\) data
• On the density of smooth functions in Sobolev-Orlicz spaces
• ANALYSIS OF A FINITE VOLUME METHOD FOR A CROSS-DIFFUSION MODEL IN POPULATION DYNAMICS
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• ON NON-NEWTONIAN FLUIDS WITH A PROPERTY OF RAPID THICKENING UNDER DIFFERENT STIMULUS
• Approximation of nonlinear wave equations with nonstandard anisotropic growth conditions
• Entropy solutions for the $p(x)$-Laplace equation
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• Density of smooth functions in W ^{k, p(x)} ( Ω )
• Hölder continuity of the gradient of p(x)-harmonic mappings
• An existence theorem for a strongly nonlinear elliptic problem in Orlicz spaces
• Regularity of nonstandard lagrangians ƒ(x, ξ)
• Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder
• Density of C^∞(Ω) inW^{1,p (x )}(Ω) with discontinuous exponent p (x )
• Variable Exponent, Linear Growth Functionals in Image Restoration
• Regularity results for a class of functionals with non-standard growth
• Mathematical modeling of electrorheological materials
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)