Non unique solutions to boundary value problems for non symmetric divergence form equations
Analysis of PDEs
2007-10-31 v2 Classical Analysis and ODEs
Abstract
We calculate explicitly solutions to the Dirichlet and Neumann boundary value problems in the upper half plane, for a family of divergence form equations with non symmetric coefficients with a jump discontinuity. It is shown that the boundary equation method and the Lax--Milgram method for constructing solutions may give two different solutions when the coefficients are sufficiently non symmetric.
Cite
@article{arxiv.0709.2255,
title = {Non unique solutions to boundary value problems for non symmetric divergence form equations},
author = {Andreas Axelsson},
journal= {arXiv preprint arXiv:0709.2255},
year = {2007}
}
Comments
Revised version. To appear in Transactions of the American Mathematical Society