On the fundamental solution of a differential operator with a singularity. (Russian) Zbl 0647.35022

Serov, V. S.

Differ. Uravn. 23, No. 3, 531-534 (1987).

A local fundamental solution of a linear elliptic differential operator of arbitrary order is constructed by means of integral equations provided that near to the singular point the coefficients are subject to conditions of Dini type. Some estimates of the fundamental solution are also derived.

Reviewer: T.Genchev

MSC:

35J35	Variational methods for higher-order elliptic equations
35A08	Fundamental solutions to PDEs
35A07	Local existence and uniqueness theorems (PDE) (MSC2000)
35A20	Analyticity in context of PDEs

Keywords:

local fundamental solution; arbitrary order; integral equations; singular point; conditions of Dini type; estimates