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On the classical solution of nonlinear elliptic equations of second order. (English. Russian original) Zbl 0682.35048

Math. USSR, Izv. 33, No. 3, 597-612 (1989); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 52, No. 6, 1272-1287 (1988).
The author proves \(C^{2+\alpha}\) solvability and derives \(C^{2+\alpha}\) apriori estimates for solutions of the Dirichlet problem for a fully nonlinear second order elliptic equation in a bounded domain \(\Omega \subset {\mathbb{R}}^ n\). His abstract results cover also the case of the Bellman equation \(\sup_{k}(L^ ku+f^ k)=0\), where the coefficients of the linear elliptic operators \(L^ k\) and the functions \(f^ k\) are supposed to be equally bounded in \(C^{\alpha}({\bar \Omega})\) and \(\alpha >0\) is supposed to be sufficiently small.
Reviewer: P.Quittner

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35B45 A priori estimates in context of PDEs
49L20 Dynamic programming in optimal control and differential games
35J25 Boundary value problems for second-order elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
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