AVERAGING ANDG-CONVERGENCE OF DIFFERENTIAL OPERATORS
Vasilii Vasil'evich Zhikov, Serguei M. Kozlov, O A Oleĭnik, Kha T'en Ngoan · Russian Mathematical Surveys · 1979
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 N γ § 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