by Grunau, Hans-Christoph, Sweers, Guido.
Series: 2006-06, Preprints
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.
polyharmonic Green function; regions of positivity; general domains
This paper was published in:
Proc. Amer. Math. Soc. 135, 3537-3546 (2007).