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

DOI10.1134/S106456241501010XzbMath1325.35033MaRDI QIDQ2353056

A. V. Podol'skii

Publication date: 7 July 2015

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

homogenizationboundary value problem\(p\)-Laplacianboundary of holes

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for higher-order elliptic equations (35J40) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Nonlinear boundary value problems for nonlinear elliptic equations (35J66)

Related Items (10)

Homogenization of the \(p\)-Laplacian with nonlinear boundary condition on critical size particles: identifying the strange term for the some non smooth and multivalued operators ⋮ On Homogenization of Nonlinear Robin Type Boundary Conditions for the n-Laplacian in n-Dimensional Perforated Domains ⋮ Characterizing the strange term in critical size homogenization: quasilinear equations with a general microscopic boundary condition ⋮ 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 \(p\) = \(n\) ⋮ Homogenization of variational inequalities for the \(p\)-Laplace operator in perforated media along manifolds ⋮ Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles ⋮ 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 \(p > n\) ⋮ Unilateral problems for thep-Laplace operator in perforated media involving large parameters ⋮ On the asymptotic limit of the effectiveness of reaction-diffusion equations in periodically structured media ⋮ Homogenization of a parabolic equation for \(p\)-Laplace operator in a domain perforated along \((n-1)\)-dimensional manifold with dynamical boundary condition specified on perforations boundary: critical case

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 limit for the boundary value problem with the \(p\)-Laplace operator and a nonlinear third boundary condition on the boundary of the holes in a perforated domain
• On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary
• On homogenization problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities
• Quasilinear Dirichlet problem in a periodically perforated domain

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