G-compactness of sequences of non-linear operators of Dirichlet problems with a variable domain of definition

Izvestiya Mathematics

Volumn 60, Issue 1, 1996, Pages 137-168

  Kovalevskii, A A ^a  

^a NONE

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EID: 21344458517     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM1996v060n01ABEH000065     Document Type: Article

References (12)

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3. E. Ya. Khruslov, "The first boundary value problem in domains with a complicated boundary for higher-order equations", Mat. Sb. 103 (1977), 614-629; English transi, in Math. USSR-Sb. 32 (1977).
4. I.V. Skrypnik, "Quasi-linear Dirichlet problem for domains with a finite-grained boundary", Dokl. Akad. Nauk Ukrain. SSR, Ser. A 1982, no. 2, 21-25. (Russian)
5. I.V. Skrypnik, Methods of studying non-linear elliptic boundary value problems, Nauka, Moscow 1990. (Russian)
6. L.S. Pankratov, "On the asymptotic behaviour of solutions of variational problems in domains with a complicated boundary", Preprint No. 11-87, FTINT Akad. Nauk Ukr. SSR, Khar'kov 1987. (Russian)
7. G. Dal Maso and A. Garroni, "A new approach to the study of limits of Dirichlet problems in perforated domains", Preprint No. 67/M, SISSA, Trieste 1993.
8. G. Dal Maso and F. Murât, "Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators", Preprint, SISSA, Trieste 1993.
9. V.V. Zhikov, "On passage to the limit in non-linear variational problems", Mat. Sb. 183:8 (1992), 47-84; English transi, in Russian Akad. Sei. Sb. Math. 76 (1993).
10. A.A. Kovalevsky, "On G-compactness of a sequence of nonlinear operators of Dirichlet problems in variable domains", Preprint No. 93.09, IAMM, Donetsk 1993.
11. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris 1969; Russian transi., Mir, Moscow 1972.
12. A.N. Kolmogorov and S. V. Fomin, Eléments of the theory of functions and functional analysis, 4th revised edition, Nauka, Moscow 1976; English transi, of 1st edition, Graylock Press, Rochester, NY 1957.