Boundary value problems for the Laplacian in convex and semiconvex domains
type: Item
instance of: scholarly article
title: Boundary value problems for the Laplacian in convex and semiconvex domains
zbMATH Open document ID: 1201.35095
author: Dorina Mitrea
author: Marius Mitrea
author: Lixin Yan
published in: Journal of Functional Analysis
publication date: 2010-03-31T00:00:00Z
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35J08
zbMATH DE Number: 5688805
zbMATH Keywords: Laplacian
zbMATH Keywords: semiconvex domain
zbMATH Keywords: convex domain
zbMATH Keywords: Lipschitz domain satisfying a uniform exterior ball condition
zbMATH Keywords: Besov and Triebel-Lizorkin spaces
zbMATH Keywords: nontangential maximal function
zbMATH Keywords: Green operator
zbMATH Keywords: Poisson problem
MaRDI profile type: Publication
full work available at URL: j.jfa.2010.01.012
OpenAlex ID: W1980465419
cites work: The Hardy–Lorentz spaces Hp,q(Rn)
cites work: $L^2$-Integrability of Second Order Derivatives for Poisson's Equation in Nonsmooth Domains.
cites work: \(L^ p\)-integrability of the second order derivatives of Green potentials in convex domains
cites work: Q4850188
cites work: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
cites work: Q4112938
cites work: Semiconcave functions, Hamilton-Jacobi equations, and optimal control
cites work: Neumann problems and isocapacitary inequalities
cites work: Hardy spaces, BMO, and boundary value problems for the Laplacian on a smooth domain in 𝐑^{𝐍}
cites work: Q4037147
cites work: \(H^ p\) theory on a smooth domain in \(\mathbb{R}^ N\) and elliptic boundary value problems
cites work: Extensions of Hardy spaces and their use in analysis
cites work: Q5568226
cites work: Un résultat de densité pour les équations de Maxwell régularisées dans un domaine lipschitzien
cites work: Estimates of harmonic measure
cites work: $L^q$-estimates for Green potentials in Lipschitz domains.
cites work: Hardy spaces and the Neumann problem in \(L^ p\) for Laplace's equation in Lipschitz domains
cites work: Area integral estimates for higher order elliptic equations and systems
cites work: Besov regularity for elliptic boundary value problems
cites work: Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
cites work: Q4215356
cites work: Compression of Wavelet Decompositions
cites work: Multiscale characterizations of Besov spaces on bounded domains
cites work: Potential techniques for boundary value problems on \(C^1\)-domains
cites work: Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains
cites work: The space Weak H¹
cites work: Interpolation Between H p Spaces: The Real Method
cites work: Potential Space Estimates for Green Potentials in Convex Domains
cites work: Regularity of the Dirichlet problem in convex domains in the plane
cites work: Third derivative estimates for Dirichlet's problem in convex domains
cites work: A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains
cites work: A local version of real Hardy spaces
cites work: Q3470840
cites work: The Green function for uniformly elliptic equations
cites work: Traces of functions in Hardy and Besov spaces on Lipschitz domains with applications to compensated compactness and the theory of Hardy and Bergman type spaces
cites work: Sobolev Estimates for the Green Potential Associated with the Robin—Laplacian in Lipschitz Domains Satisfying a Uniform Exterior Ball Condition
cites work: The Neumann problem on Lipschitz domains
cites work: The inhomogeneous Dirichlet problem in Lipschitz domains
cites work: On the regularity of the solution of the Poisson problem on a domain with boundary locally similar to the boundary of a convex open set
cites work: Q5448226
cites work: Q3219291
cites work: Q4305610
cites work: The Neumann problem for elliptic equations with non-smooth coefficients
cites work: Q4362327
cites work: Q3141911
cites work: Sharp estimates for Green potentials on non-smooth domains
cites work: Q5527340
cites work: Q5680498
cites work: Q3788519
cites work: The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations
cites work: A generalization of Dahlberg's theorem concerning the regularity of harmonic Green potentials
cites work: On the Besov regularity of conformal maps and layer potentials on nonsmooth domains.
cites work: The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains
cites work: Q3645944
cites work: Coercive energy estimates for differential forms in semi-convex domains

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Multi-layer potentials and boundary problems for higher-order elliptic systems in Lipschitz domains

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Dirichlet integrals and Gaffney-Friedrichs inequalities in convex domains

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Lipschitz Domains, Domains with Corners, and the Hodge Laplacian

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Boundary value problems for the Stokes system in arbitrary Lipschitz domains

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: $H^{p}$ spaces over open subsets of $R^{n}$

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Hardy-Sobolev spaces and maximal functions

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Q4694399

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Q4893982

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: A relationship between the Dirichlet and regularity problems for elliptic equations

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Q5840384

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Q5607484

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Sopra una classe di equazioni ellittiche a coefficienti misurabili

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Partial differential equations. 3: Nonlinear equations

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Q3336200

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Entropy Numbers and Approximation Numbers in Function Spaces, II

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains

Boundary value problems for the Laplacian in convex and semiconvex domains (cites work)
cites work: On the atomic decomposition for Hardy spaces

Boundary value problems for the Laplacian in convex and semiconvex domains (DOI)
DOI: 10.1016/J.JFA.2010.01.012