Weak interior second order derivative estimates for degenerate nonlinear elliptic equations

N. V. Krylov, Luis A. Caffarelli

Research output: Contribution to journalArticlepeer-review

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Abstract

We are dealing with the Dirichlet problem for elliptic Bellman equations with underlying linear operators. Under some mild assumptions we prove that second order derivatives of a solution can be estimated in the interior of the domain via estimates on the boundary of the function itself and its derivatives up to the second order, the maJdmum of the second order normal derivative entering the estimate with arbitrary small coefficient.

Original languageEnglish (US)
Pages (from-to)133-156
Number of pages24
JournalDifferential and Integral Equations
Volume7
Issue number1
StatePublished - Jan 1994

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