Homogenization of boundary value problems in plane domains with frequently alternating type of nonlinear boundary conditions: critical case

DOI10.1134/S1064562418030225zbMath1403.35033OpenAlexW2884266624WikidataQ129560327 ScholiaQ129560327MaRDI QIDQ1673708

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

Publication date: 13 September 2018

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

Full work available at URL: https://doi.org/10.1134/s1064562418030225

zbMATH Keywords

boundary homogenizationnonlinear Robin-type condition

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (5)

A time-dependent strange term arising in homogenization of an elliptic problem with rapidly alternating Neumann and dynamic boundary conditions specified at the domain boundary: the critical case ⋮ Unnamed Item ⋮ Homogenization of the boundary value problem for the Poisson equation with rapidly oscillating nonlinear boundary conditions: Space dimension \(n \geq 3\), critical case ⋮ Homogenization of a boundary value problem for the \(n\)-Laplace operator on a \(n\)-dimensional domain with rapidly alternating boundary condition type: the critical case ⋮ Homogenization of the optimal control problem for the Dirichlet cost functional and the Poisson state problem with rapidly alternating boundary conditions in critical case

Cites Work

• Homogenization of the boundary value problem for the Laplace operator in a domain perforated along (\(n\) - 1)-dimensional manifold with nonlinear Robin type boundary condition on the boundary of arbitrary shaped holes: critical case
• Boundary homogenization of a variational inequality with nonlinear restrictions for the flux on small regions lying on a part of the boundary
• Semi-linear second-order elliptic equations in \(L^1\)
• Homogenization of a variational inequality for the Laplace operator with nonlinear restriction for the flux on the interior boundary of a perforated domain
• Homogenization of variational inequalities of Signorini type for the \(p\)-Laplacian in perforated domains when \(p\in(1, 2)\)
• Averaging of variational inequalities for the Laplacian with nonlinear restrictions along manifolds
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