Nonhomogeneous biharmonic problem in the half-space, $L^p$ theory and generalized solutions

Chérif Amrouche (1) , Yves Raudin (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

In this paper, we study the biharmonic equation in the half-space $\mathbb{R^N_+})$, with $N \geq 2$. We prove in $L^p$ theory, with $1 < p < \infty$, existence and uniqueness results. We consider data and give solutions which live in weighted Sobolev spaces.

Mots clés: Weighted Sobolev spaces; Biharmonic problem; Half-space; Weighted Sobolev spaces.

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Yves Raudin. Nonhomogeneous biharmonic problem in the half-space, $L^p$ theory and generalized solutions. 2007. ⟨hal-00199654⟩