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October 2011 Boundary integral operators and boundary value problems for Laplace’s equation
TongKeun Chang, John L. Lewis
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Ark. Mat. 49(2): 239-276 (October 2011). DOI: 10.1007/s11512-010-0135-z

Abstract

In this paper, we define boundary single and double layer potentials for Laplace’s equation in certain bounded domains with d-Ahlfors regular boundary, considerably more general than Lipschitz domains. We show that these layer potentials are invertible as mappings between certain Besov spaces and thus obtain layer potential solutions to the regularity, Neumann, and Dirichlet problems with boundary data in these spaces.

Funding Statement

Research of both authors was partially supported by NSF grant DMS-0552281. Part of this research was carried out while the first author was a visitor at the University of Kentucky. He thanks the University of Kentucky for the gracious hospitality extended to him during his visit.

Citation

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TongKeun Chang. John L. Lewis. "Boundary integral operators and boundary value problems for Laplace’s equation." Ark. Mat. 49 (2) 239 - 276, October 2011. https://doi.org/10.1007/s11512-010-0135-z

Information

Received: 4 September 2009; Published: October 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1262.31009
MathSciNet: MR2826943
Digital Object Identifier: 10.1007/s11512-010-0135-z

Rights: 2010 © Institut Mittag-Leffler

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Vol.49 • No. 2 • October 2011
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