AVERAGING AND<i>G</i>-CONVERGENCE OF DIFFERENTIAL OPERATORS

Abstract

CONTENTS Introduction Chapter I. G-convergence of operators § 1. G-convergence of abstract operators § 2. G-convergence of elliptic operators of higher order. The N-condition. Auxiliary propositions § 3. Basic properties of G-convergence of elliptic operators § 4. Some examples § 5. Further results on the G-convergence of elliptic operators Chapter II. The averaging of elliptic operators § 1. Auxiliary results. Statements of the main theorems on averaging § 2. Analysis of the equations for the functions Nγ § 3. Proofs of the main theorems on averaging of elliptic operators Chapter III. Some applications § 1. The asymptotic behaviour at infinity of solutions of second-order elliptic equations § 2. The asymptotic behaviour of fundamental solutions of second-order parabolic equations. Stabilization References