ON PASSAGE TO THE LIMIT IN NONLINEAR VARIATIONAL PROBLEMS
Vasilii Vasil'evich Zhikov · Sbornik Mathematics · 1993
A study is made of variational problems with convex Lagrangians subordinate to a nonstandard estimate The concepts of -convergence and -convergence are introduced for Lagrangians corresponding to boundary value problems of the first and second types. It is proved that the indicated class of Lagrangians is compact with respect to -convergence and with respect to -convergence. Applications to compactness theorems and to various concrete averaging problems are given.Bibliography: 22 titles.