Homogenization of variational inequality for the Laplace operator with nonlinear constraint on the flow in a domain perforated by arbitrary shaped sets. Critical case

DOI10.1007/s10958-018-3888-8zbMath1402.35035OpenAlexW2807034846MaRDI QIDQ1661639

M. N. Zubova, Tatiana A. Shaposhnikova

Publication date: 16 August 2018

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-018-3888-8

zbMATH Keywords

critical sizeLaplace operator, nonlinear constraint

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Methods involving semicontinuity and convergence; relaxation (49J45) 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)

Related Items (2)

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 limit for the diffusion equation in a domain perforated along \((n - 1)\)-dimensional manifold with dynamic conditions on the boundary of the perforations: critical case

Cites Work

• 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
• 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
• 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 the asymptotic limit of the effectiveness of reaction-diffusion equations in periodically structured media
• 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 \(p\in(1, 2)\)
• The Poisson Equation with Nonautonomous Semilinear Boundary Conditions in Domains with Many Time Holes
• Averaging of variational inequalities for the Laplacian with nonlinear restrictions along manifolds
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