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

TongKeun Chang Department of Mathematics, Korea Institute of Advanced Studies John L. Lewis Mathematics Department, University of Kentucky

Analysis of PDEs mathscidoc:1701.03020

Arkiv for Matematik, 49, (2), 239-276, 2009.9
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.
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@inproceedings{tongkeun2009boundary,
  title={Boundary integral operators and boundary value problems for Laplace’s equation},
  author={TongKeun Chang, and John L. Lewis},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203630797937006},
  booktitle={Arkiv for Matematik},
  volume={49},
  number={2},
  pages={239-276},
  year={2009},
}
TongKeun Chang, and John L. Lewis. Boundary integral operators and boundary value problems for Laplace’s equation. 2009. Vol. 49. In Arkiv for Matematik. pp.239-276. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203630797937006.
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