Boundedness of the negative part of biharmonic Green's functions under Dirichlet boundary conditions in general domains

DOI10.1016/j.crma.2008.12.013zbMath1168.35008OpenAlexW2072099861MaRDI QIDQ1004548

Frédéric Robert, Hans-Christoph Grunau

Publication date: 11 March 2009

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2008.12.013

zbMATH Keywords

Green's functionsDirichlet boundary conditionspositivity preserving property

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Fundamental solutions to PDEs (35A08)

Related Items (2)

Nonlinear questions in clamped plate models ⋮ Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions

Cites Work

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• Estimates for Green function and Poisson kernels of higher-order Dirichlet boundary value problems
• Decay and local eventual positivity for biharmonic parabolic equations
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• A partial differential equation arising in conformal mapping
• Continuation of biharmonic functions by reflection
• Pointwise lower bounds on the heat kernels of higher order elliptic operators
• Positivity for Perturbations of Polyharmonic Operators with Dirichlet Boundary Conditions in Two Dimensions
• Regions of positivity for polyharmonic Green functions in arbitrary domains
• Separating positivity and regularity for fourth order Dirichlet problems in 2d-domains
• ISOLATION OF SINGULARITIES OF THE GREEN'S FUNCTION
• On a Question of Hadamard Concerning Super‐Biharmonic Functions

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