Electron. J. Differential Equations,
Vol. 2017 (2017), No. 309, pp. 123.
Layer potentials for general linear elliptic systems
Ariel Barton
Abstract:
In this article we construct layer potentials for elliptic differential
operators using the BabuskaLaxMilgram 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
wellposedness of boundary value problems and invertibility of layer potentials.
Submitted March 27, 2017. Published December 14, 2017.
Math Subject Classifications: 35J58, 31B10.
Key Words: Higher order differential equation; layer potentials; Dirichlet problem;
Neumann problem.
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Ariel Barton
Department of Mathematical Sciences
309 SCEN, University of Arkansas
Fayetteville, AR 72701, USA
email: aeb019@uark.edu

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