Homogenization of variational inequalities of Signorini type for the \(p\)-Laplacian in perforated domains when \(p\in(1, 2)\)

DOI10.1134/S1064562417020132zbMath1370.35036OpenAlexW2598738872MaRDI QIDQ2399517

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

Publication date: 24 August 2017

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

Full work available at URL: https://doi.org/10.1134/s1064562417020132

zbMATH Keywords

nonlinear constraints

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators (35J87)

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Homogenization of variational inequality for the Laplace operator with nonlinear constraint on the flow in a domain perforated by arbitrary shaped sets. Critical case ⋮ Homogenization of boundary value problems in plane domains with frequently alternating type of nonlinear boundary conditions: critical case ⋮ Homogenization of the boundary value problem for the Laplace operator in a perforated domain with a rapidly oscillating nonhomogeneous Robin-type condition on the boundary of holes in the critical case ⋮ Characterizing the strange term in critical size homogenization: quasilinear equations with a general microscopic boundary condition ⋮ Unexpected regionally negative solutions of the homogenization of Poisson equation with dynamic unilateral boundary conditions: critical symmetric particles ⋮ Homogenization of variational inequalities for the \(p\)-Laplace operator in perforated media along manifolds ⋮ Unnamed Item ⋮ 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 \(p > n\) ⋮ On the asymptotic limit of the effectiveness of reaction-diffusion equations in periodically structured media ⋮ Homogenization of a boundary-value problem in a domain perforated by cavities of arbitrary shape with a general nonlinear boundary condition on their boundaries: the case of critical values of the parameters ⋮ 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 \(p\)-Laplace operator in perforated media with nonlinear restrictions on the boundary of the perforations: A critical case
• Regularity for a more general class of quasilinear equations
• Homogenization of a variational inequality for the Laplace operator with nonlinear restriction for the flux on the interior boundary of a perforated domain
• Linear and quasilinear elliptic equations
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• On a Nonlinear Parabolic Problem Arising in Some Models Related to Turbulent Flows

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