Maximum principles for the polyharmonic equation on Lipschitz domains

DOI10.1007/BF02345828zbMath0844.35013MaRDI QIDQ1904296

Jill Pipher, Gregory C. Verchota

Publication date: 19 December 1995

Published in: Potential Analysis (Search for Journal in Brave)

zbMATH Keywords

Agmon-Miranda maximum principle

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60)

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Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey ⋮ Area integral estimates for higher order elliptic equations and systems ⋮ Boundary value problems and integral operators for the bi-Laplacian in non-smooth domains ⋮ Polyharmonic capacity and Wiener test of higher order ⋮ Necessary and sufficient conditions for the solvability of the \(L^p\) Dirichlet problem on Lipschitz domains ⋮ Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains ⋮ An overview of the method of fundamental solutions -- solvability, uniqueness, convergence, and stability ⋮ Regularity of solutions to the polyharmonic equation in general domains ⋮ The \(L^{p}\) boundary value problems on Lipschitz domains ⋮ Nonsymmetric systems on nonsmooth planar domains ⋮ Solutions of fixed sign of higher-order inhomogeneous equations of mixed elliptic-hyperbolic type ⋮ Sign-definiteness of solution to inhomogeneous higher-order equation of mixed parabolic-hyperbolic type ⋮ The Ẇ−1,p Neumann problem for higher order elliptic equations ⋮ Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains ⋮ On estimates of biharmonic functions on Lipschitz and convex domains ⋮ Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation ⋮ The inhomogeneous Dirichlet problem for \(\Delta^2\) in Lipschitz domains ⋮ Removable singularity of the polyharmonic equation ⋮ Boundary-value Problems for Higher-order Elliptic Equations in Non-smooth Domains

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