06-06
Regions of positivity for polyharmonic Green functions in arbitrary domains
by Grunau, Hans-Christoph; Sweers, Guido
Preprint series: 06-06, Preprints
The paper is published: Proc. Amer. Math. Soc. 135, 3537-3546 (2007).
- MSC:
- 35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
- 35B50 Maximum principles
- 35J40 Boundary value problems for higher-order, elliptic equations
Abstract: The Green function for the biharmonic operator on bounded domains with zero Dirichlet boundary conditions is in general not of fixed sign. However, by extending an idea of Z.~Nehari, we are able to identify regions of positivity for Green functions of polyharmonic operators. In particular, the biharmonic Green function is considered in all space dimensions. As a consequence we see that the negative part of any such Green function is somehow small compared with the singular positive part.
Keywords: polyharmonic Green function; regions of positivity; general domains
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