Geodesic
On passage to the limit in nonlinear variational problems
Sbornik. Mathematics, Tome 76 (1993) no. 2, pp. 427-459 Cet article a éte moissonné depuis la source Math-Net.Ru

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A study is made of variational problems with convex Lagrangians $f(x,\xi)$ subordinate to a nonstandard estimate \begin{gather*} -c_0+c_1|\xi|^{\alpha_1}\leqslant f(x,\xi)\leqslant c_0+c_2|\xi|^{\alpha_2}, \\ c_0\geqslant 0, c_1>0, \quad c_2>0, \quad 1<\alpha_1\leqslant\alpha_2. \end{gather*} The concepts of $\Gamma_1$-convergence and $\Gamma_2$-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 $\Gamma_1$-convergence and with respect to $\Gamma_2$-convergence. Applications to compactness theorems and to various concrete averaging problems are given. 
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     author = {V. V. Zhikov},
     title = {On passage to the~limit in nonlinear variational problems},
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     volume = {76},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_76_2_a9/}
}
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V. V. Zhikov. On passage to the limit in nonlinear variational problems. Sbornik. Mathematics, Tome 76 (1993) no. 2, pp. 427-459. http://geodesic.mathdoc.fr/item/SM_1993_76_2_a9/

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