On fundamental solutions of elliptic equations

Abstract

In this paper we prove: Let L be an elliptic operator in (x, t) with constant coefficients, the coefficients of the lower derivatives being zero, and let Lo be the operator obtained from L by deleting all the terms involving t-derivatives. Let K(x, t) be a fundamental solution of Lu = 0. Then fr [K(x, t) S(x, t) ]dt is a fundamental solution of Lov=O where S(x, t) is a certain simple expression introduced for reasons of convergence. A similar result for parabolic equations was proved by Eidelman [I]. Consider the elliptic equation of order 2m