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Uniform anti-maximum principle for polyharmonic boundary value problems
Author(s):
Philippe
Clément;
Guido
Sweers
Journal:
Proc. Amer. Math. Soc.
129
(2001),
467-474.
MSC (1991):
Primary 35J40, 35B50;
Secondary 31B30
Posted:
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.
References:
- 1.
- Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976), no. 4, 620-709. MR 57:7269
- 2.
- Amann, H., Linear and quasilinear parabolic problems, Vol. I. Abstract linear theory, Monographs in Mathematics 89, Birkhäuser Verlag, Basel, 1995. MR 96g:34088
- 3.
- Boggio, T., Sulle funzioni di Green d'ordine m, Rend. Circ. Mat. Palermo 20 (1905), 97-135.
- 4.
- Clément, Ph., and Peletier, L.A., An anti-maximum principle for second order elliptic operators, J. Differ. Equations 34 (1979), 218-229. MR 83c:35034
- 5.
- Clément, Ph., and Sweers, G., Uniform anti-maximum principles, to appear in J. Differ. Equations.
- 6.
- Grunau, H.-Ch. and Sweers, G., Positivity for equations involving polyharmonic elliptic operators with Dirichlet boundary conditions, Math. Ann. 307 (1997), 589-626. MR 98g:35058
- 7.
- Grunau, H.-Ch. and Sweers, G., The maximum principle and positive principal eigenfunctions for polyharmonic equations, in Reaction Diffusion systems, Marcel Dekker Inc., New York 1997, p 163-182. MR 98h:35050
- 8.
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- 10.
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 is sharp for the antimaximum principle, J. Differential Equations 134 (1997), 148-153. MR 98a:35011 - 12.
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- 13.
- Triebel, H., ''Interpolation Theory, Function Spaces, Differential Operators'', North-Holland, Amsterdam, 1978. MR 80i:46032b
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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:
10.1090/S0002-9939-00-05768-3
PII:
S 0002-9939(00)05768-3
Keywords:
Anti-maximum principle,
higher order elliptic,
polyharmonic
Received by editor(s):
April 22, 1999
Posted:
August 28, 2000
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2000,
American Mathematical Society
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