Regions of positivity for polyharmonic Green functions in arbitrary domains

Grunau, Hans-Christoph; Sweers, Guido

doi:10.1090/S0002-9939-07-08851-X

Regions of positivity for polyharmonic Green functions in arbitrary domains
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by Hans-Christoph Grunau and Guido Sweers PDF

Proc. Amer. Math. Soc. 135 (2007), 3537-3546 Request permission

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.

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