Third derivative estimates for Dirichlet's problem in convex domains

DOI10.1215/S0012-7094-94-07312-2zbMath0792.35034OpenAlexW1547096564MaRDI QIDQ1325163

Stephen J. Fromm, David S. Jerison

Publication date: 7 August 1994

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-94-07312-2

zbMATH Keywords

bounded convex domain

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

Uniform Level Set Estimates for Ground State Eigenfunctions ⋮ On the boundedness of first derivatives for solutions to the Neumann-Laplace problem in a convex domain ⋮ Hardy spaces and regularity for the inhomogeneous Dirichlet and Neumann problems ⋮ The shape of the level sets of the first eigenfunction of a class of two-dimensional Schrödinger operators ⋮ Boundedness of the Hessian of a Biharmonic Function in a Convex Domain ⋮ Boundary value problems for the Laplacian in convex and semiconvex domains ⋮ Asymptotic formula for solutions to elliptic equations near the Lipschitz boundary ⋮ Behavior of Solutions to the Dirichlet Problem for Elliptic Systems in Convex Domains ⋮ Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain

Cites Work

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• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Hardy spaces and the Neumann problem in \(L^ p\) for Laplace's equation in Lipschitz domains
• A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\)
• Regularity of the Dirichlet problem in convex domains in the plane
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Potential Space Estimates for Green Potentials in Convex Domains
• An Extended Principle of the Maximum for Harmonic Functions in 3-Dimensions
• Convexity properties of solutions to some classical variational problems

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