Elliptic problems with $L^1$-data  in the half-space

Chérif Amrouche; Huy Hoang Nguyen

doi:10.3934/dcdss.2012.5.369

Article Contents

2012, Volume 5, Issue 3: 369-397. Doi: 10.3934/dcdss.2012.5.369

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Elliptic problems with $L^1$-data in the half-space

Chérif Amrouche^1, and
Huy Hoang Nguyen^2,

1.
Laboratoire de Mathématiques Appliquées, CNRS UMR 5142, Université de Pau et des Pays de l’Adour, IPRA, Avenue de l’Université, 64000 Pau
2.
Departamento de Matematica, IMECC - Universidade Estadual de Campinas, Caixa Postal 6065, Campinas, SP 13083-970

Received: August 31, 2010

Revised: January 31, 2011

Published: May 2012

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Abstract

In this paper, we study the div-curl-grad operators and some elliptic problems in the half-space $\mathbb{R}^n_+$, with $n\geq 2$. We consider data in weighted Sobolev spaces and in $L^1$.

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Mathematics Subject Classification: 35J25, 35J47.

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References

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