Uniform anti-maximum principle for polyharmonic boundary value problems

DOI10.1090/S0002-9939-00-05768-3zbMath0959.35044OpenAlexW1778122044MaRDI QIDQ4517484

Philippe Clément, Guido Sweers

Publication date: 22 November 2000

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-00-05768-3

zbMATH Keywords

anti-maximum principlehigher-order ellipticpolyharmonic Dirichlet problems

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Maximum principles in context of PDEs (35B50) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30)

Related Items (9)

On the existence of bounded solutions for a nonlinear elliptic system ⋮ Existence theory for stochastic power law fluids ⋮ Uniform bounds for higher-order semilinear problems in conformal dimension ⋮ Positivity and anti-maximum principles for elliptic operators with mixed boundary conditions ⋮ Quasi uniformity for the abstract Neumann antimaximum principle and applications with a priori estimates ⋮ MAXIMUM PRINCIPLES AROUND AN EIGENVALUE WITH CONSTANT EIGENFUNCTIONS ⋮ Unnamed Item ⋮ Separating positivity and regularity for fourth order Dirichlet problems in 2d-domains ⋮ An operator theoretic approach to uniform (anti-)maximum principles

Cites Work

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• \(L^ n\) is sharp for the anti-maximum principle
• An anti-maximum principle for second order elliptic operators
• Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions
• Uniform anti-maximum principles
• An abstract form of maximum and anti-maximum principles of Hopf's type
• Errata: Fixed Point Theorems and Nonlinear Eigenvalue Problems in Ordered Banach Spaces

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