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On algebraic and geometric conditions in the theory of Hessian equations

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Abstract

The paper is a kind of survey which contains a description of new algebraic and geometric structures together with fragments of a technique developed in the theory of Hessian equations. Our principal concern here is the m-Hessian evolutionary equations, and we formulate some existence and nonexistence theorems of solutions to the first initial boundary value problems in C 2(Q̄ T ) for such equations.

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Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, St.Petersburg State University, 7-9 Universitetskaya nab., 199034, St.Petersburg, Russia

    N. M. Ivochkina

  2. St.Petersburg State University of Architecture and Civil Engineering, 2-nd Krasnoarmeiskaya St. 4, 190005, St.Petersburg, Russia

    N. V. Filimonenkova

  3. St.Petersburg Polytechnic University, 29 Polytechnicheskaya St., 195251, St.Petersburg, Russia

    N. V. Filimonenkova

Authors
  1. N. M. Ivochkina
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  2. N. V. Filimonenkova
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Correspondence to N. M. Ivochkina.

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To Professor Andrzej Granas

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Ivochkina, N.M., Filimonenkova, N.V. On algebraic and geometric conditions in the theory of Hessian equations. J. Fixed Point Theory Appl. 16, 11–25 (2014). https://doi.org/10.1007/s11784-015-0217-4

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  • DOI: https://doi.org/10.1007/s11784-015-0217-4

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