Corpus ID: 119677010

Layer potentials for general linear elliptic systems

@article{Barton2017LayerPF,
  title={Layer potentials for general linear elliptic systems},
  author={Ariel Barton},
  journal={arXiv: Analysis of PDEs},
  year={2017}
}
  • A. Barton
  • Published 20 March 2017
  • Mathematics
  • arXiv: Analysis of PDEs
In this paper we construct layer potentials for elliptic differential operators using the Lax-Milgram theorem, without recourse to the fundamental solution; this allows layer potentials to be constructed in very general settings. We then generalize several well known properties of layer potentials for harmonic and second order equations, in particular the Green's formula, jump relations, adjoint relations, and Verchota's equivalence between well-posedness of boundary value problems and… Expand
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