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
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
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