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Communications on Pure and Applied Analysis (CPAA)
 

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

Pages: 1295 - 1333, Volume 7, Issue 6, November 2008      doi:10.3934/cpaa.2008.7.1295

 
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Dorina Mitrea - University of Missouri-Columb, Columbia, MO 65211, United States (email)
Marius Mitrea - University of Missouri-Columbia, Columbia, MO 65211, United States (email)
Sylvie Monniaux - Université Aix-Marseille 3, F-13397 Marseille Cédex 20, France (email)

Abstract: 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.

Keywords:  Exterior derivative, divergence equation, differential forms, Poisson problem, Dirichlet condition, Lipschitz domain, Sobolev, Besov, Triebel-Lizorkin spaces.
Mathematics Subject Classification:  Primary: 58J32, 35F15; Secondary: 58J10, 35N10.

Received: January 2008;      Revised: June 2008;      Available Online: August 2008.