Non unique solutions to boundary value problems for non symmetric divergence form equations

Details Non unique solutions to boundary value problems for non symmetric divergence form equations Non unique solutions to boundary value problems for non symmetric divergence form equations

2007-09-14

arxiv.org/abs/0709.2255v2

Mathematics

Analysis of PDEs

Revised version. To appear in Transactions of the American Mathematical Society

Scientific paper

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.

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