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Uniform anti-maximum principle for polyharmonic boundary value problems


Authors: Philippe Clément and Guido Sweers
Journal: Proc. Amer. Math. Soc. 129 (2001), 467-474
MSC (1991): Primary 35J40, 35B50; Secondary 31B30
Published electronically: August 28, 2000
MathSciNet review: 1800235
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Abstract:

A uniform anti-maximum principle is obtained for iterated polyharmonic Dirichlet problems. The main tool, combined with regularity results for weak solutions, is an estimate for positive functions in negative Sobolev norms.


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Additional Information

Philippe Clément
Affiliation: Department of Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
Email: clement@twi.tudelft.nl

Guido Sweers
Affiliation: Department of Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
Email: sweers@twi.tudelft.nl

DOI: https://doi.org/10.1090/S0002-9939-00-05768-3
Keywords: Anti-maximum principle, higher order elliptic, polyharmonic
Received by editor(s): April 22, 1999
Published electronically: August 28, 2000
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2000 American Mathematical Society