On the regularity for the Laplace equation and the Stokes system

Chérif Amrouche (1) , Maria Angeles Rodriguez-Bellido (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 EDAN - Departamento de Ecuaciones Differenciales y Analysis numérico [Sevilla]

The purpose of this work is to show a broad framework in which the theory of very weak solutions for the Dirichlet stationary problem for the Laplace and Stokes equations in bounded domains of Rn, n ≥ 2, could be developed. Broad in the sense of giving the more general spaces in which data can be taken in order to obtain a very weak solution and define properly the trace of such solution. Density arguments and a functional framework will be necessary, as well as classical regularity results in the Lp -Sobolev spaces that will be generalized here.

Mots clés: Stokes equations; Very weak solutions; Stationary Solutions

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Maria Angeles Rodriguez-Bellido. On the regularity for the Laplace equation and the Stokes system. 2011. ⟨hal-00629123⟩