Non existence of critical scales in the homogenization of the problem with \(p\)-Laplace diffusion and nonlinear reaction in the boundary of periodically distributed particles in \(n\)-dimensional domains when \(p > n\)

DOI10.1007/s13398-017-0381-zzbMath1390.35013OpenAlexW2589782005MaRDI QIDQ1742906

Jesús Ildefonso Díaz, A. V. Podol'skii, Tatiana A. Shaposhnikova, David Gómez-Castro

Publication date: 12 April 2018

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-017-0381-z

zbMATH Keywords

homogenization\(p\)-Laplace diffusionnon-critical sizesnon-linear boundary reaction

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Quasilinear elliptic equations (35J62) Quasilinear elliptic equations with (p)-Laplacian (35J92) Nonlinear boundary value problems for nonlinear elliptic equations (35J66)

Related Items (3)

Characterizing the strange term in critical size homogenization: quasilinear equations with a general microscopic boundary condition ⋮ On \(p\)-Laplacian reaction-diffusion problems with dynamical boundary conditions in perforated media ⋮ Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis ``nano-composite membranes

Cites Work

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• Homogenization of boundary value problems in perforated domains with the third boundary condition and the resulting change in the character of the nonlinearity in the problem
• Homogenization for the \(p\)-Laplacian in an \(n\)-dimensional domain perforated by very thin cavities with a nonlinear boundary condition on their boundary in the case \(p\) = \(n\)
• On homogenization problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities
• Solution continuation and homogenization of a boundary value problem for the \(p\)-Laplacian in a perforated domain with a nonlinear third boundary condition on the boundary of holes
• Homogenization of variational inequalities of Signorini type for the \(p\)-Laplacian in perforated domains when \(p\in(1, 2)\)

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