The Green Function for Elliptic Systems in Two Dimensions |
| |
Authors: | J L Taylor S Kim |
| |
Institution: | 1. Department of Mathematics , Murray State University , Murray , Kentucky , USA;2. Department of Computational Science and Engineering , Yonsei University , Seoul , Korea |
| |
Abstract: | We construct the fundamental solution or Green function for a divergence form elliptic system in two dimensions with bounded and measurable coefficients. Our main goal is construct the Green function for the operator with mixed boundary conditions in a Lipschitz domain. Thus we specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We require a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary conditions. Our proof proceeds by defining a variant of the space BMO(Ω) that is adapted to the boundary conditions and showing that the solution exists in this space. We also give a construction of the Green function with Neumann boundary conditions and the fundamental solution in the plane. |
| |
Keywords: | BMO Green function Mixed boundary conditions |
|
|