Weighted estimates in 𝐿² for Laplace’s equation on Lipschitz domains

DOI10.1090/S0002-9947-04-03608-6zbMath1145.35363OpenAlexW1598190983MaRDI QIDQ4663488

Zhongwei Shen

Publication date: 31 March 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-04-03608-6

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) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

One problem of the Navier type for the Stokes system in planar domains ⋮ The \(L^{p}\) Robin problem for Laplace equations in Lipschitz and (semi-)convex domains ⋮ Lp Neumann problem for some Schrödinger equations in (semi-)convex domains ⋮ Regularity for Robin boundary problems of Laplace equations and Hardy spaces on \(C^1\) and (semi-)convex domains ⋮ The \(L^{p}\) boundary value problems on Lipschitz domains ⋮ The mixed problem in \(L^{p}\) for some two-dimensional Lipschitz domains ⋮ Unique solvability of the Neumann problem with weighted boundary data on a bounded \(C^{1}\) domain ⋮ Necessary and sufficient conditions for the solvability of the Neumann and the regularity problems in \(L^p\) of some Schrödinger equations on Lipschitz domains ⋮ Weighted \(L^p\) boundary value problems for Laplace's equation on (semi-)convex domains ⋮ The mixed problem in Lipschitz domains with general decompositions of the boundary ⋮ Neumann functions for second order elliptic systems with measurable coefficients

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