November  2008, 7(6): 1295-1333. doi: 10.3934/cpaa.2008.7.1295

The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains

1. 

University of Missouri-Columb, Columbia, MO 65211, United States

2. 

University of Missouri-Columbia, Columbia, MO 65211, United States

3. 

Université Aix-Marseille 3, F-13397 Marseille Cédex 20, France

Received  January 2008 Revised  June 2008 Published  August 2008

We formulate and solve the Poisson problem for the exterior derivative operator with Dirichlet boundary condition in Lipschitz domains, of arbitrary topology, for data in Besov and Triebel-Lizorkin spaces.
Citation: Dorina Mitrea, Marius Mitrea, Sylvie Monniaux. The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains. Communications on Pure & Applied Analysis, 2008, 7 (6) : 1295-1333. doi: 10.3934/cpaa.2008.7.1295
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