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Siberian Mathematical Journal

, Volume 28, Issue 6, pp 872–884 | Cite as

A class of higher-order elliptic equations degenerate on a portion of the boundary

  • L. A. Bagirov
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Elliptic Equation 
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Literature Cited

  1. 1.
    M. I. Vishik and V. V. Grushin, “On a class of higher-order degenerate elliptic equations,” Mat. Sb.,79, No. 1, 3–36 (1969).Google Scholar
  2. 2.
    H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam-New York-Oxford (1978).Google Scholar
  3. 3.
    V. A. Kondrat'ev, “Boundary-value problems for elliptic equations in domains with conical or angular points,” Trudy Mosk. Mat. Obshch.,16, 209–292 (1967).Google Scholar
  4. 4.
    L. A. Bagirov, “On strong solutions of a class of degenerate elliptic equations of high order in domains with a piecewise-smooth boundary” [in Russian], Moscow (1986). Deposited in VINITI, No. 1077-B86.Google Scholar
  5. 5.
    A. V. Bitsadze, Some Classes of Partial Differential Equations [in Russian], Nauka, Moscow (1981).Google Scholar
  6. 6.
    O. A. Oleinik and E. V. Radkevich, Second Order Equations with Nonnegative Characteristic Form [in Russian], WINITI, Moscow (1971).Google Scholar
  7. 7.
    M. M. Smirnov, Degenerate Elliptic and Hyperbolic Equations [in Russian], Nauka, Moscow (1966).Google Scholar
  8. 8.
    S. A. Tersenov, Introduction to the Theory of Equations Degenerate on the Boundary [in Russian], Nauka, Novosibirsk (1973).Google Scholar
  9. 9.
    K. I. Babenko, “On the theory of an equation of mixed type,” Doctoral Dissertation, Physical-Mathematical Sciences, V. A. Steklov Math. Inst., Moscow (1952).Google Scholar
  10. 10.
    M. I. Vishik and V. V. Grushin, “Degenerate elliptic differential and pseudodifferential operators,” Usp. Mat. Nauk,25, No. 4, 29–56 (1970).Google Scholar
  11. 11.
    V. P. Glushko, “Solvability theorems for boundary-value problems for a class of degenerate elliptic equations of high order,” in: Partial Differential Equations [in Russian], Math. Inst., Siberian Branch, Academy of Sciences of the USSR, Novosibirsk (1980), pp. 49–68 (S. L. Sobolev Seminar Proceedings, No. 2).Google Scholar
  12. 12.
    I. A. Kipriyanov, “On a class of singular elliptic operators. I,” Differents. Uravn.,7, No. 11, 2066–2077 (1971); II, Sin. Mat. Zh.,14, No. 3, 560–581 (1973).Google Scholar
  13. 13.
    I. I. Lizorkin and S. M. Nikol'skii, “Coercive properties of elliptic equations with degeneracy, Variational method,” Trudy Mat. Inst. V. A. Steklova,157, Moscow (1981).Google Scholar
  14. 14.
    P. Bolley and J. Camus, “Sur une classe d'operateurs elliptiques et degeneres a plusieurs variables,” Bull. Soc. Math. France (Suppl. Mem.),34, 55–140 (1973).Google Scholar
  15. 15.
    M. S. Baouendi, “Sur une classe d'operateurs elliptiques degeneres,” Bull. Soc. Math. France,95, 45–87 (1967).Google Scholar
  16. 16.
    L. A. Bagirov, “Boundary-value problems for a class of elliptic equations of high order on a plane and degenerate on a portion of the boundary,” Dokl. Akad. Nauk SSSR,290, No. 2, 270–274 (1986).Google Scholar
  17. 17.
    L. A. Bagirov, “Boundary-value problems for degenerate elliptic equations in domains with a nonsmooth boundary,” Usp. Mat. Nauk,38, No. 5, 151 (1983).Google Scholar
  18. 18.
    V. G. Maz'ya and B. A. Plamenevskii, “Estimates in Lp and in Holder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary-value problems in domains with singular points on the boundary,” Math. Nachr.,81, 25–82 (1978).Google Scholar
  19. 19.
    M. S. Agranovich and M. I. Vishik, “Elliptic problems with a parameter and parabolic problems of a general form,” Usp. Mat. Nauk,19, No. 5, 53–161 (1964).Google Scholar
  20. 20.
    P. M. Blekher, “On operators depending meromorphically on a parameter,” Vestn. Mosk. Gos. Univ., Ser. I, Mat., Mekh., No. 5, 30–36 (1969).Google Scholar
  21. 21.
    E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge Univ. Press (1952).Google Scholar

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© Plenum Publishing Corporation 1988

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  • L. A. Bagirov

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