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

Chérif Amrouche; Yves Raudin

doi:10.3934/cpaa.2007.6.957

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2007, Volume 6, Issue 4: 957-982. Doi: 10.3934/cpaa.2007.6.957

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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

Received: August 2006

Revised: May 2007

Published: December 2007

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Abstract

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.

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Mathematics Subject Classification: 35D05, 35D10, 35J35, 35J40.

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