The Neumann problem in \(L^p\) on Lipschitz and convex domains

DOI10.1016/j.jfa.2008.06.032zbMath1180.35202OpenAlexW2069852979MaRDI QIDQ952505

Zhongwei Shen, Aekyoung Shin Kim

Publication date: 12 November 2008

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2008.06.032

zbMATH Keywords

convex domainNeumann problemLipschitz domain

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25)

Related Items (15)

The Neumann problem of Laplace's equation in semiconvex domains ⋮ One problem of the Navier type for the Stokes system in planar domains ⋮ Large deviations in the quantum quasi-1D jellium ⋮ Homogenization of elliptic systems with Neumann boundary conditions ⋮ The \(L^{p}\) Robin problem for Laplace equations in Lipschitz and (semi-)convex domains ⋮ \(L^p\) Neumann problems in homogenization of general elliptic operators ⋮ The regularity problems with data in Hardy-Sobolev spaces for singular Schrödinger equation in Lipschitz domains ⋮ Lp Neumann problem for some Schrödinger equations in (semi-)convex domains ⋮ Nonlinear Neumann-transmission problems for Stokes and Brinkman equations on Euclidean Lipschitz domains ⋮ Equivalent conditions for the consistency of the Helmholtz decomposition of Muckenhoupt \(A_p\)-weighted \(L_p\)-spaces ⋮ The Neumann problem and Helmholtz decomposition in convex domains ⋮ 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 global regularity estimates for elliptic problems with Robin boundary conditions in Lipschitz domains ⋮ Weighted \(L^p\) boundary value problems for Laplace's equation on (semi-)convex domains ⋮ The 2D Euler-Boussinesq equations in planar polygonal domains with Yudovich's type data

Cites Work

• The \(L^p\) Dirichlet problem for elliptic systems on Lipschitz domains
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• Hardy spaces and the Neumann problem in \(L^ p\) for Laplace's equation in Lipschitz domains
• Potential techniques for boundary value problems on \(C^1\)-domains
• A geometric approach to the Calderón-Zygmund estimates
• Necessary and sufficient conditions for the solvability of the \(L^p\) Dirichlet problem on Lipschitz domains
• The \(L^{p}\) boundary value problems on Lipschitz domains
• Riesz transform on manifolds and heat kernel regularity
• On necessary and sufficient conditions for 𝐿^{𝑝}-estimates of Riesz transforms associated to elliptic operators on ℝⁿ and related estimates
• Weighted norm inequalities for the Lusin area integral and the nontangential maximal functions for functions harmonic in a Lipschitz domain
• The Neumann problem on Lipschitz domains
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