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Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth
Authors:
O. Druet and F. Robert
Journal:
Proc. Amer. Math. Soc. 134 (2006), 897-908
MSC (2000):
Primary 58E30, 58J05, 35J35
Posted:
September 28, 2005
MathSciNet review:
2180908
Full-text PDF Free Access
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Abstract: We are concerned in this paper with the bubbling phenomenon for nonlinear fourth-order four-dimensional PDE's. The operators in the equations are perturbations of the bi-Laplacian. The nonlinearity is of exponential growth. Such equations arise naturally in statistical physics and geometry. As a consequence of our theorem we get a priori bounds for solutions of our equations.
References
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Chang, S.Y.A. and Yang, P.C., On a fourth order curvature invariant. Spectral problems in geometry and arithmetic (Iowa City, IA, 1997), 9-28, Contemp. Math., 237, Amer. Math. Soc., Providence, RI, 1999. MR 1710786 (2001b:58056)
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Additional Information
O. Druet
Affiliation:
Unité de Mathématiques Pures et Appliquées, École Normale Supérieure de Lyon, 46, allée d'Italie, 69364 Lyon cedex 7, France
Email:
odruet@umpa.ens-lyon.fr
F. Robert
Affiliation:
Université de Nice Sophia-Antipolis, Laboratoire J. A. Dieudonné, Parc Valrose, 06108 Nice cedex 2, France
Email:
frobert@math.unice.fr
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08330-9
PII:
S 0002-9939(05)08330-9
Keywords:
Concentration estimates,
fourth-order equations,
compactness
Received by editor(s):
September 29, 2004
Posted:
September 28, 2005
Communicated by:
Jozef Dodziuk
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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