A condition for the compactness of operators in a certain class and its application to the analysis of the solubility of non-local problems for elliptic equations

Sbornik Mathematics

Volumn 193, Issue 5-6, 2002, Pages 649-668

  Gushchin, A K ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

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EID: 0036621506     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM2002v193n05ABEH000649     Document Type: Article

References (24)

1. A.K. Gushchin and V.P. Mikhaǐlov, "On solvability of nonlocal problems for a second-order elliptic equation", Mat. Sb. 185:1 (1994), 121-160; English transl. in Russian Acad. Sci. Sb. Math. 81 (1995).
2. A.K. Gushchin and V.P. Mikhaǐlov, "On solvability of nonlocal problems for a second-order elliptic equation", Mat. Sb. 185:1 (1994), 121-160; English transl. in Russian Acad. Sci. Sb. Math. 81 (1995).
3. A.K. Gushchin and V.P. Mikhaǐlov, "On the continuity of the solutions of a class of non-local problems for an elliptic equation", Mat. Sb. 186:2 (1995), 37-58; English transl. in Sb. Math. 186 (1996).
4. A.K. Gushchin and V.P. Mikhaǐlov, "On the univalent solvability of nonlocal problems for an elliptic equation", Dokl. Ross. Akad. Nauk 351 (1996), 7-8; English transl. in Dokl. Math. 154 (1996).
5. A.K. Gushchin and V.P. Mikhaǐlov, "On the univalent solvability of nonlocal problems for an elliptic equation", Dokl. Ross. Akad. Nauk 351 (1996), 7-8; English transl. in Dokl. Math. 154 (1996).
6. A.K. Gushchin, "Some properties of the solutions of the Dirichlet problem for a second-order elliptic equation", Mat. Sb. 189:7 (1998), 53-90; English transl. in Sb. Math. 189 (1997).
7. A.V. Bitsadze and A.A. Samarskiǐ, "On some simple generalizations of linear elliptic boundary problems", Dokl. Akad. Nauk SSSR 185 (1969), 739-740; English transl. in Soviet Math. Dokl. 10 (1969).
8. A.V. Bitsadze and A.A. Samarskiǐ, "On some simple generalizations of linear elliptic boundary problems", Dokl. Akad. Nauk SSSR 185 (1969), 739-740; English transl. in Soviet Math. Dokl. 10 (1969).
9. A.K. Gushchin, "On the Dirichlet problem for a second-order elliptic equation", Mat. Sb. 137 (179):1 (1988), 19-64; English transl. in Math. USSR-Sb. 65 (1990).
10. A.K. Gushchin, "On the Dirichlet problem for a second-order elliptic equation", Mat. Sb. 137 (179):1 (1988), 19-64; English transl. in Math. USSR-Sb. 65 (1990).
11. V.P. Mikhaǐlov, "Dirichlet's problem for a second-order elliptic equation", Differentsial'nye Uravneniya 12:10 (1976), 1877-1891; English transl. in Differential Equations 12 (1976).
12. A.K. Gushchin and V.P. Mikhaǐlov, "On the existence of boundary values of solutions of an elliptic equation", Mat. Sb. 182 (1991), 787-810; English transl. in Math. USSR-Sb. 73 (1992).
13. A.K. Gushchin and V.P. Mikhaǐlov, "On the existence of boundary values of solutions of an elliptic equation", Mat. Sb. 182 (1991), 787-810; English transl. in Math. USSR-Sb. 73 (1992).
14. J.B. Garnett, Bounded analytic functions, Pure Appl. Math., vol. 96, Academic Press, New York 1981.
15. L. Carleson, "An interpolation problem for bounded analytic functions", Amer. J. Math. 80 (1958), 921-930.
16. p-estimates for (pluri-)subharmonic functions", Math. Scand. 20 (1967), 65-78.
17. B.P. Paneyakh, "Certain nonlocal boundary-value problems for linear differential operators", Mat. Zametki 35 (1984), 425-434; English transl. in Math. Notes 35 (1984).
18. E.I. Galakhov and A.L. Skubachevskiǐ, "On non-negative contractive semigroups with non-local conditions", Mat. Sb. 189:1 (1998), 45-78; English transl. in Sb. Math. 189 (1998).
19. A.K. Gushchin, "Condition of complete continuity of operators arising in nonlocal problems for elliptic equations", Dokl. Ross. Akad. Nauk 373 (2000), 161-163; English transl. in Dokl. Math. 62 (2000).
20. A.K. Gushchin, "Condition of complete continuity of operators arising in nonlocal problems for elliptic equations", Dokl. Ross. Akad. Nauk 373 (2000), 161-163; English transl. in Dokl. Math. 62 (2000).
21. E. DeGiorgi, "Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari", Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. (5) 3 (1957), 25-43.
22. J. Nash, "Continuity of solutions of parabolic and elliptic equations", Amer. J. Math. 80 (1958), 931-954.
23. O. A. Ladyzhenskaya and N.N. Ural'tseva, Linear and quasilinear elliptic equations, Nauka, Moscow 1973; English transl. of 1st ed., Academic Press, New York 1968.
24. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin 1983.