Construction of Fundamental Solutions for Certain Degenerated Elliptic Operators

Abstract

The purpose of this memoire is to construct fundamental solutions for certain degenerated dliptic operators A defined in a domain Ω of Rn. Operators A that we treat are of the same type as ones in Baouendi-Goulaouic [1] and in GoulaouicShimakura [2]. In other words, they have, roughly speaking, the following properties (see the hypotheses [H-1]~[H-5] in §2): (a) They are second-order linear differential operators with smooth coefficients.