On the Existence of Smooth Solutions for Fully Nonlinear Parabolic Equations with Measurable "Coefficients" without Convexity Assumptions

Hongjie Dong, N. V. Krylov

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in any cylindrical smooth domain with smooth boundary data one can find an approximating equation which has a unique continuous solution with the first derivatives bounded and the second spacial derivatives locally bounded. The approximating equation is constructed in such a way that it modifies the original one only for large values of the unknown function and its spacial derivatives.

Original languageEnglish (US)
Pages (from-to)1038-1068
Number of pages31
JournalCommunications in Partial Differential Equations
Volume38
Issue number6
DOIs
StatePublished - Jun 1 2013

Keywords

  • Bellman's equations
  • Finite differences
  • Fully nonlinear parabolic equations

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