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Regions of positivity for polyharmonic Green functions in arbitrary domains |
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| Authors: | Hans-Christoph Grunau Guido Sweers |
| Institution: | Fakultät für Mathematik, Otto--von--Guericke--Universität, Postfach 4120, 39016 Magdeburg, Germany ; Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany; and Delft Institute of Applied Mathematics, Delft University of Technology, PO Box 5031, 2600 GA Delft, The Netherlands |
| 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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