Journal of Mathematical Sciences

, Volume 143, Issue 2, pp 2875–2882 | Cite as

Weak first-order interior estimates and Hessian equations

  • N. M. Ivochkina


Development of the modern theory of fully nonlinear, second-order partial differential equations has amazingly enriched the classical collection of ideas and methods. In this paper, we construct first-order interior a priori estimates of new type for solutions of Hessian equations. These estmates are applied to present the most transparent version of Krylov’s method and its tight connection with fully nonlinear equations. Bibliography: 11 titles.


Dirichlet Problem Viscosity Solution Bellman Equation Nonlinear Elliptic Equation Admissible Solution 
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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • N. M. Ivochkina
    • 1
  1. 1.St.Petersburg State University of Architecture and Civil EngineeringRussia

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