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Boundary integral methods for harmonic differential forms in Lipschitz domains

Author(s): Dorina Mitrea; Marius Mitrea
Journal: Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 92-97.
MSC (1991): Primary 35J55; Secondary 42B20
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Abstract: A layer potential based approach for boundary value problems for harmonic differential forms in nonsmooth domains is developed. This allows a complete and unified treatment of several fundamental problems in potential theory.

References:

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P. E. Conner, The Neumann's problem for differential forms on Riemannian manifolds, vol. 20, Memoirs of Amer. Math. Soc., (third printing), 1956. MR 17:1197e
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D. Jerison and C. Kenig, The Neumann problem on Lipschitz domains, Bull. Amer. Math. Soc. 4 (1981), 203--207. MR 84a:35064
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D. Mitrea, M. Mitrea, and J. Pipher, Vector potential theory on nonsmooth domains in ${\mathbb {R}}^{3}$ and applications to electromagnetic scattering, to appear in the Journal of Fourier Analysis and Applications, Fall, (1995).
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C. B. Morrey, Jr., Multiple integrals in the calculus of variations, Heidelberg, New York, Springer-Verlag, Berlin, 1966. MR 34:2380
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M. E. Taylor, Partial differential equations, Springer-Verlag, 1996. CMP 96:14
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G. Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains, J. Funct. Anal. 59 (1984), 572--611. MR 86e:35038

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Additional Information:

Dorina Mitrea
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211
Email: dorina@sidon.math.missouri.edu

Marius Mitrea
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211
Email: marius@msindy2.math.missouri.edu

DOI: 10.1090/S1079-6762-96-00012-1
PII: S 1079-6762(96)00012-1
Keywords: Harmonic differential forms, Lipschitz domains, layer potentials
Received by editor(s): July 25, 1996
Communicated by: Michael Taylor
Copyright of article: Copyright 1996, American Mathematical Society

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