Approximate Green's Function for the Conductivity Equation With Conormal Coefficient

Abstract

We construct an approximate Green's function for $L_{\gamma }=\nabla \cdot \gamma (x)\nabla u(x)$, which belongs to a class of Fourier Integral Operators (FIOs) associated to two canonical relations. This leads to analysis of the composition of two FIOs, associated to a canonical relation with a zero section problem. The resulting composition is a sum of two FIOs, each associated to two intersecting canonical relations.

29 pages