\(\varGamma \)-convergence and homogenization of functionals in Sobolev spaces with variable exponents

DOI10.1016/j.jmaa.2007.12.035zbMath1357.49052OpenAlexW2150877206MaRDI QIDQ2481917

Brahim Amaziane, Leonid S. Pankratov, Stanislav N. Antontsev, Andrey L. Piatnitski

Publication date: 15 April 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.12.035

zbMATH Keywords

homogenizationvariable exponent\(\varGamma \)-convergence

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Variational methods for second-order elliptic equations (35J20) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (11)

A gamma convergence approach to the critical Sobolev embedding in variable exponent spaces ⋮ A pointwise estimate of the solution to the \(p\)-Laplace evolution equation ⋮ Three-scale convergence for processes in heterogeneous media ⋮ Homogenization in Sobolev spaces with nonstandard growth: brief review of methods and applications ⋮ On the asymptotic behaviour of a variable exponent power law magnetostatic problem ⋮ Structural stability for variable exponent elliptic problems. I: The \(p(x)\)-Laplacian kind problems ⋮ Improved bounds on the supremum of autoconvolutions ⋮ Deterministic homogenization of nonlinear degenerate elliptic operators with nonstandard growth ⋮ Elliptic boundary value problems with nonstandard growth conditions ⋮ A Variational Technique to the Homogenization of Maxwell Equations ⋮ Homogenization of \(p\)-Laplacian in perforated domain

Cites Work

• Orlicz spaces and modular spaces
• Topology of the space \(\mathcal L^{p(t)}([0,t)\)]
• Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functions
• On generalized Orlicz-Sobolev space
• On Lavrentiev's phenomenon
• On some variational problems
• An introduction to \(\Gamma\)-convergence
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Geometric aspects of averaging
• Regularity results for a class of functionals with non-standard growth
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