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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Regions of positivity for polyharmonic Green functions in arbitrary domains

Author(s): Hans-Christoph Grunau; Guido Sweers
Journal: Proc. Amer. Math. Soc. 135 (2007), 3537-3546.
MSC (2000): Primary 35J65, 35B50, 35J40
Posted: July 3, 2007
MathSciNet review: 2336568
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Abstract | References | Similar articles | Additional information

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: 10.1090/S0002-9939-07-08851-X
PII: S 0002-9939(07)08851-X
Received by editor(s): February 13, 2006
Received by editor(s) in revised form: July 7, 2006
Posted: July 3, 2007
Dedicated: Dedicated to Prof. J. Serrin on the occasion of his 80th birthday
Communicated by: Walter Craig
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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