Fully Nonlinear, Uniformly Elliptic Equations Under Natural Structure Conditions
- 1 August 1983
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 278 (2) , 751-769
- https://doi.org/10.2307/1999182
Abstract
We derive first and second derivative estimates for classical solutions of fully nonlinear, uniformly elliptic equations which are subject to natural structure conditions analogous to those proposed and treated by Ladyzhenskaya and Ural’tseva for quasilinear equations. As an application we extend recent work of Evans and Lions on the Bellman equation for families of linear operators to families of quasilinear operators.Keywords
This publication has 6 references indexed in Scilit:
- Classical Solutions of The Hamilton-Jacobi-Bellman Equation for Uniformly Elliptic OperatorsTransactions of the American Mathematical Society, 1983
- Classical solutions of fully nonlinear, convex, second‐order elliptic equationsCommunications on Pure and Applied Mathematics, 1982
- Resolution analytique des problemes de Bellman-DirichletActa Mathematica, 1981
- Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equationsInventiones Mathematicae, 1980
- Optimal Stochastic Switching and the Dirichlet Problem for the Bellman EquationTransactions of the American Mathematical Society, 1979
- On the Approximation of Linear Elliptic Differential Equations by Difference Equations with Positive CoefficientsJournal of Mathematics and Physics, 1952