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On a class of equations of monge-ampere type

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Abstract

We prove that the Dirichlet problem is solvable in a generalized sense for a class of nonlinear elliptic equations and related equations of Monge-Ampère type. Bibliography: 14 titles.

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Literature Cited

  1. N. M. Ivochkina, “Solution of the Dirichlet problem for certain equations of Monge-Ampère type,”Mat. Sb.,128, (170), 403–415 (1985).

    MathSciNet  Google Scholar 

  2. L. Caffarelli, L. Nirenberg, and J. Spruck, “The Dirichlet problem for nonlinear second-order elliptic equations III. Functions of the eigenvalues of the Hessian”,Acta Math.,155, No. 3-4, 261–304 (1985).

    MathSciNet  Google Scholar 

  3. N. V. Krylov, “On the first boundary-value problem for nonlinear degenerate elliptic equations”,Izv. Akad. Nauk SSSR, Ser. Mat.,51, No. 2, 242–269 (1987).

    MATH  Google Scholar 

  4. N. M. Ivochkina, “Solution of the Dirichlet problem for the curvature equation of orderm”.Dokl. Akad. Nauk SSSR,299, No. 1, 35–38 (1988).

    MATH  MathSciNet  Google Scholar 

  5. L. Caffarelli, L. Nirenberg, and J. Spruck, “Nonlinear second-order elliptic equations V. The Dirichlet problem for Weingarten hypersurfaces”,Comm. Pure Appl. Math.,41, 47–70 (1988).

    MathSciNet  Google Scholar 

  6. N. M. Ivochkina, “Solution of the Dirichlet problem for the curvature equation of orderm”,Mat. Sb.,180, No. 7, 867–887 (1989).

    MATH  Google Scholar 

  7. N. S. Trudinger, “The Dirichlet problem for the prescribed curvature equations”,Arch. Rat. Mech. Anal.,155, No. 3-4, 261–304 (1985).

    Google Scholar 

  8. N. M. Ivochkina, “Solution of the Dirichlet problem for the curvature equation of orderm”,Alg. Anal., No. 3, 195–220 (1990).

    Google Scholar 

  9. N. M. Ivochkina, “Variational problems connected with operators of Monge-Ampère type”,Zap. Nauch. Sem. LOMI Akad. Nauk SSSR,167, 186–189 (1988).

    MATH  Google Scholar 

  10. N. S. Trudinger, “A priori bounds and necessary conditions for solvability of prescribed curvature equations”,Man. Math.,67, No. 1, 99–112 (1990).

    MATH  MathSciNet  Google Scholar 

  11. N. M. Ivochkina, “Description of the cones of stability generated by differential operators of Monge-Ampère type”,Mat. Sb.,122, 165–275 (1983).

    MathSciNet  Google Scholar 

  12. L. Gårding, “An inequality for hyperbolic polynomials”,J. Math. Mech.,8, 957–965 (1959).

    MATH  MathSciNet  Google Scholar 

  13. N. M. Ivochkina, “An integral method of barrier functions and the Dirichlet problem for equations with operators of Monge-Ampère type”,Mat. Sb.,112 (156) 193–206 (1980).

    MATH  MathSciNet  Google Scholar 

  14. O. A. Ladyzhenskaya and N. N. Ural'tseva, “Linear and quasilinear elliptic equations”, Academic Press, New York (1968).

    Google Scholar 

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Translated fromProblemy Matematicheskogo Analiza, No. 13, 1992, pp. 89–106.

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Ivochkina, N.M., Prokof'eva, S.I. & Yakunina, G.V. On a class of equations of monge-ampere type. J Math Sci 73, 663–673 (1995). https://doi.org/10.1007/BF02364944

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