Mixed exterior Laplace's problem

Chérif Amrouche (1) , Florian Bonzom (1)

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

In [3], authors study Dirichlet and Neumann problems for the Laplace operator in exterior domains of $\mathbb{R^n})$. This paper extends this study to the resolution of a mixed exterior Laplace's problem. Here, we give existence, unicity and regularity results in $L^p$'s theory with $1 < p < 1$, in weighted Sobolev spaces.

Mots clés: Weighted Sobolev spaces; Laplacian; Mixed boundary conditions; Poincaré type inequality

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Florian Bonzom. Mixed exterior Laplace's problem. 2007. ⟨hal-00199734⟩