Arkiv för Matematik

  • Ark. Mat.
  • Volume 49, Number 2 (2011), 239-276.

Boundary integral operators and boundary value problems for Laplace’s equation

TongKeun Chang and John L. Lewis

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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.

Note

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.

Article information

Source
Ark. Mat., Volume 49, Number 2 (2011), 239-276.

Dates
Received: 4 September 2009
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907147

Digital Object Identifier
doi:10.1007/s11512-010-0135-z

Mathematical Reviews number (MathSciNet)
MR2826943

Zentralblatt MATH identifier
1262.31009

Rights
2010 © Institut Mittag-Leffler

Citation

Chang, TongKeun; Lewis, John L. Boundary integral operators and boundary value problems for Laplace’s equation. Ark. Mat. 49 (2011), no. 2, 239--276. doi:10.1007/s11512-010-0135-z. https://projecteuclid.org/euclid.afm/1485907147


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