The Poisson's problem for the Laplacian with Robin boundary condition in non-smooth domains

DOI10.4171/RMI/453zbMath1160.35389MaRDI QIDQ854549

Loredana Lanzani, Osvaldo Méndez

Publication date: 5 December 2006

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1148492180

zbMATH Keywords

Triebel-Lizorkin spacesBesov spacesRobin conditionLamé systemnon-smooth domainsboundary layer potentialsPoisson's problemregularity of PDE's

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Integral operators (47G10) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items

On the Robin-transmission boundary value problems for the nonlinear Darcy-Forchheimer-Brinkman and Navier-Stokes systems ⋮ Transmission problem for the Laplace equation and the integral equation method ⋮ Regularity for Robin boundary problems of Laplace equations and Hardy spaces on \(C^1\) and (semi-)convex domains ⋮ Boundary value problems of Robin type for the Brinkman and Darcy-Forchheimer-Brinkman systems in Lipschitz domains ⋮ Potential techniques and regularity of boundary value problems in exterior non-smooth domains ⋮ Dirichlet problem for a nonlinear generalized Darcy-Forchheimer-Brinkman system in Lipschitz domains ⋮ Integral representation of a solution to the Stokes-Darcy problem ⋮ Weighted global regularity estimates for elliptic problems with Robin boundary conditions in Lipschitz domains ⋮ Positive solutions of elliptic equations with nonlinear boundary conditions ⋮ The Robin problem for the scalar Oseen equation ⋮ Poisson problems for semilinear Brinkman systems on Lipschitz domains in \(\mathbb{R}^n\)

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