New estimates for the div-curl-grad operators and elliptic problems with L1-data in the whole space and in the half-space

Chérif Amrouche (1) , Huy Hoang Nguyen (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 IMECC - Instituto de Matemática, Estatística e Computação Científica [Brésil]

In this paper, we study the div-curl-grad operators and some elliptic problems in the whole space R^n and in the half-space R^n_+, with n >= 2. We consider data in weighted Sobolev spaces and in L1.

Mots clés: Div-curl-grad operators; Elliptic; Half-space; Weighted Sobolev spaces

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Huy Hoang Nguyen. New estimates for the div-curl-grad operators and elliptic problems with L1-data in the whole space and in the half-space. 2011. ⟨hal-00559615⟩