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Variational problems connected with Monge-Ampere type operators

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In this note we describe a geometric problem leading to Monge-Ampere type operators. Some variational problems and theorems on their solvability are formulated.

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Literature cited

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    N. M. Ivochkina, “Solution of the Dirichlet problem for Monge-Ampere type equations”, Mat. Sb.,128 (170), No. 3, 403–415 (1985).

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    L. Caffarelli, L. Nirenberg, and J. Spruck, “The Dirichlet problem for nonlinear secondorder elliptic equations. III. Functions of the eigenvalues of the Hessian”, Acta Math.,155, Nos. 3–4, 261–301 (1985).

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    N. V. Krylov, “First boundary problem for nonlinear degenerate elliptic equations”, Izv. Akad. Nauk SSSR,51, No. 2, 242–269 (1987).

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 167, pp. 186–189, 1988.

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Ivochkina, N.M. Variational problems connected with Monge-Ampere type operators. J Math Sci 52, 2861–2863 (1990).

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  • Variational Problem
  • Type Operator
  • Geometric Problem