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September  2009, 8(5): 1709-1723. doi: 10.3934/cpaa.2009.8.1709

Regularity of the extremal solution for a biharmonic problem with general nonlinearity

Guillaume Warnault 1,

1. 

Laboratoire Amiénois de Mathématiques Fondamentale et Appliquée, Faculté de Mathématiques et d' Informatique, 33, rue Saint-Leu 80039 Amiens Cedex 1, France

Received  July 2008 Revised  January 2009 Published  April 2009

We consider the class of radial solutions of semilinear equations $\Delta^2 u=\lambda f(u)$ in the unit ball of $\mathbb R^N$. It is the class of stable solutions which includes minimal solutions and extremal solution. We establish the regularity of this extremal solution for $N\leq 9$. Our regularity results do not depend on the specific nonlinearity $f$.
Keywords: regularity., Biharmonic operator, extremal solution.
Mathematics Subject Classification: Primary: 31B30; Secondary: 74B.
Citation: Guillaume Warnault. Regularity of the extremal solution for a biharmonic problem with general nonlinearity. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1709-1723. doi: 10.3934/cpaa.2009.8.1709
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