Homogenization of unbounded singular integrals in \(W^{1,\infty}\)

DOI10.1007/s11587-011-0124-yzbMath1304.49029arXiv0912.5408OpenAlexW2086804353MaRDI QIDQ473269

Omar Anza Hafsa, Jean-Philippe Mandallena

Publication date: 24 November 2014

Published in: Ricerche di Matematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.5408

zbMATH Keywords

homogenization\(\Gamma\)-convergence\(L^1\)-strong convergenceperiodic multiple integrals

Mathematics Subject Classification ID

Existence theories for free problems in two or more independent variables (49J10) Methods involving semicontinuity and convergence; relaxation (49J45) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (10)

Stochastic homogenization of nonconvex unbounded integral functionals with convex growth ⋮ Integral representation of unbounded variational functionals on Sobolev spaces ⋮ Radial extension of \(\Gamma\)-limits ⋮ Homogenization of unbounded integrals with quasiconvex growth ⋮ A relaxation result in the vectorial setting and power law approximation for supremal functionals ⋮ Relaxation of nonconvex unbounded integrals with general growth conditions in Cheeger-Sobolev spaces ⋮ Homogenization of nonconvex unbounded singular integrals ⋮ Radial representation of lower semicontinuous envelope ⋮ Homogenization of nonconvex integrals with convex growth ⋮ On the theory of relaxation in nonlinear elasticity with constraints on the determinant

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Relaxation of variational problems in two-dimensional nonlinear elasticity
• Global-local subadditive ergodic theorems and application to homogenization in elasticity.
• Homogenization of nonconvex integral functionals and cellular elastic materials
• Convexity conditions and existence theorems in nonlinear elasticity
• Implicit partial differential equations
• Homogenization of multiparameter integrals
• Relaxation theorems in nonlinear elasticity
• The lower quasiconvex envelope of the stored energy function for an elastic crystal
• On the homogenization of singular integrals
• On the lower semicontinuous quasiconvex envelope for unbounded integrands (I)
• Ergodic theorems for superadditive processes.
• A sharp version of Zhang’s theorem on truncating sequences of gradients
• Multi-parameter homogenization by localization and blow-up
• Relaxation of singular functionals defined on Sobolev spaces
• On the integral representation of relaxed functionals with convex bounded constraints

This page was built for publication: Homogenization of unbounded singular integrals in \(W^{1,\infty}\)