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December  2007, 6(4): 957-982. doi: 10.3934/cpaa.2007.6.957

Singular boundary conditions and regularity for the biharmonic problem in the half-space

Chérif Amrouche 1, and  Yves Raudin 1,

1. 

Laboratoire de Mathématiques Appliquées, CNRS UMR 5142, Université de Pau et des Pays de l’Adour, IPRA, Avenue de l’Université, 64000 Pau, France, France

Received  August 2006 Revised  May 2007 Published  September 2007

In this paper, we are interested in some aspects of the biharmonic equation in the half-space $\mathbb R^N_+$, with $N\geq 2$. We study the regularity of generalized solutions in weighted Sobolev spaces, then we consider the question of singular boundary conditions. To finish, we envisage other sorts of boundary conditions.
Keywords: half-space, Biharmonic problem, weighted Sobolev spaces..
Mathematics Subject Classification: 35D05, 35D10, 35J35, 35J4.
Citation: Chérif Amrouche, Yves Raudin. Singular boundary conditions and regularity for the biharmonic problem in the half-space. Communications on Pure and Applied Analysis, 2007, 6 (4) : 957-982. doi: 10.3934/cpaa.2007.6.957
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