Another Method to Evaluate Green Functions for Elliptic Equations

Abstract

It is well known that the resolvent kernel for a strongly elliptic operator with constant coefficients, which is the inverse Fourier transform of the related symbol, satisfies the exponential decay estimate. We derive it by the formula that expresses the resolvent in terms of the integration with respect to spectral parameter of a high power of the resolvent, whose kernel can be evaluated by the standard method. This approach also works when the elliptic operator is defined on a domain and has variable coefficients.