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

DOI10.1134/S1064562417060229zbMath1391.35041OpenAlexW2782457367MaRDI QIDQ1707157

Tatiana A. Shaposhnikova, A. V. Podol'skii

Publication date: 28 March 2018

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

Full work available at URL: https://doi.org/10.1134/s1064562417060229

zbMATH Keywords

nonlinear Robin-type condition

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (4)

Homogenization of boundary value problems in plane domains with frequently alternating type of nonlinear boundary conditions: critical case ⋮ Unnamed Item ⋮ Appearance of a nonlocal monotone operator in transmission conditions when homogenizing the Poisson equation in a domain perforated along an \((n - 1)\)-dimensional manifold by sets of arbitrary shape and critical size with nonlinear dynamic boundary conditions on the boundary of perforations ⋮ 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

Cites Work

• Homogenization problem in a domain perforated by tiny isoperimetric holes with nonlinear Robin type boundary conditions
• 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
• Averaging of boundary-value problem in domain perforated along \((n - 1)\)-dimensional manifold with nonlinear third type boundary conditions on the boundary of cavities
• 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
• On homogenization of nonlinear Robin type boundary conditions for cavities along manifolds and associated spectral problems
• Averaging of variational inequalities for the Laplacian with nonlinear restrictions along manifolds
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