Ariel Barton
Abstract:
In this article we construct layer potentials for elliptic differential
operators using the Babuska-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 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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