1 December 2004 Sharp Hodge decompositions, Maxwell's equations, and vector Poisson problems on nonsmooth, three-dimensional Riemannian manifolds
Marius Mitrea
Duke Math. J. 125(3): 467-547 (1 December 2004). DOI: 10.1215/S0012-7094-04-12322-1

Abstract

We solve three basic potential theoretic problems: Hodge decompositions for vector fields, Poisson problems for the Hodge Laplacian, and inhomogeneous Maxwell equations in arbitrary Lipschitz subdomains of a smooth, compact, three-dimensional, Riemannian manifold. In each case we derive sharp estimates on Sobolev-Besov scales and establish integral representation formulas for the solution. The proofs rely on tools from harmonic analysis and algebraic topology, such as Calderón-Zygmund theory and de Rham theory.

Citation

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Marius Mitrea. "Sharp Hodge decompositions, Maxwell's equations, and vector Poisson problems on nonsmooth, three-dimensional Riemannian manifolds." Duke Math. J. 125 (3) 467 - 547, 1 December 2004. https://doi.org/10.1215/S0012-7094-04-12322-1

Information

Published: 1 December 2004
First available in Project Euclid: 18 November 2004

zbMATH: 1073.31006
MathSciNet: MR2166752
Digital Object Identifier: 10.1215/S0012-7094-04-12322-1

Subjects:
Primary: 31C12 , 35Q60 , 58A14 , 58J32
Secondary: 31B10, , 35J25, , 42B20, , 46E35

Rights: Copyright © 2004 Duke University Press

Vol.125 • No. 3 • 1 December 2004
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