Layer potentials for general linear elliptic systems
Date
2017-12-14
Authors
Barton, Ariel
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Higher order differential equation, Layer potentials, Dirichlet problem, Neumann problem
Citation
Barton, A. (2017). Layer potentials for general linear elliptic systems. <i>Electronic Journal of Differential Equations, 2017</i>(309), pp. 1-23.
Rights
Attribution 4.0 International