Optimal estimates from below for biharmonic Green functions

DOI10.1090/S0002-9939-2010-10740-2zbMath1220.35027arXiv1103.0651MaRDI QIDQ3005627

Guido Sweers, Hans-Christoph Grunau, Frédéric Robert

Publication date: 9 June 2011

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

Full work available at URL: https://arxiv.org/abs/1103.0651

zbMATH Keywords

estimates from belowbiharmonic Green function

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Fundamental solutions to PDEs (35A08) Green's functions for elliptic equations (35J08)

Related Items (9)

Differences between fundamental solutions of general higher order elliptic operators and of products of second order operators ⋮ On sign preservation for clotheslines, curtain rods, elastic membranes and thin plates ⋮ Positivity for the clamped plate equation under high tension ⋮ A biharmonic converse to Krein-Rutman: a maximum principle near a positive eigenfunction ⋮ Note on a sign-dependent regularity for the polyharmonic Dirichlet problem ⋮ Classical solutions up to the boundary to some higher order semilinear Dirichlet problems ⋮ A maximum principle for a fourth-order Dirichlet problem on smooth domains ⋮ Optimal estimates from below for Green functions of higher order elliptic operators with variable leading coefficients ⋮ A biharmonic equation with singular nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• Estimates for Green function and Poisson kernels of higher-order Dirichlet boundary value problems
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions
• The clamped-plate equation for the Limac con
• Continuation of biharmonic functions by reflection
• On the reflection principle for polyharmonic functions
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• From Brownian Motion to Schrödinger’s Equation
• 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

This page was built for publication: Optimal estimates from below for biharmonic Green functions