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Regions of positivity for polyharmonic Green functions in arbitrary domains


Authors: Hans-Christoph Grunau and Guido Sweers
Journal: Proc. Amer. Math. Soc. 135 (2007), 3537-3546
MSC (2000): Primary 35J65, 35B50, 35J40
DOI: https://doi.org/10.1090/S0002-9939-07-08851-X
Published electronically: July 3, 2007
MathSciNet review: 2336568
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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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Additional Information

Hans-Christoph Grunau
Affiliation: Fakultät für Mathematik, Otto–von–Guericke–Universität, Postfach 4120, 39016 Magdeburg, Germany
Email: Hans-Christoph.Grunau@mathematik.uni-magdeburg.de

Guido Sweers
Affiliation: 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
Email: gsweers@math.uni-koeln.de, G.H.Sweers@tudelft.nl

DOI: https://doi.org/10.1090/S0002-9939-07-08851-X
Received by editor(s): February 13, 2006
Received by editor(s) in revised form: July 7, 2006
Published electronically: July 3, 2007
Dedicated: Dedicated to Prof. J. Serrin on the occasion of his 80th birthday
Communicated by: Walter Craig
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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