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

Dorina Mitrea; Marius Mitrea; Sylvie Monniaux

doi:10.3934/cpaa.2008.7.1295

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2008, Volume 7, Issue 6: 1295-1333. Doi: 10.3934/cpaa.2008.7.1295

This issue Previous Article The inhomogeneous PME in several space dimensions. Existence and uniqueness of finite energy solutions Next Article Convexity of level curves for solutions to semilinear elliptic equations

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

1.
University of Missouri-Columb, Columbia, MO 65211
2.
University of Missouri-Columbia, Columbia, MO 65211
3.
Université Aix-Marseille 3, F-13397 Marseille Cédex 20

Received: January 2008

Revised: June 2008

Published: November 2008

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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.

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Mathematics Subject Classification: Primary: 58J32, 35F15; Secondary: 58J10, 35N10.

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