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

被引：12

作者：

Dong, Hongjie ^{[1
]}

Krylov, N. V. ^{[2
]}

机构：

[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[2] Univ Minnesota, Dept Math, Minneapolis, MN 55455 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2013年 / 38卷 / 06期

基金：

美国国家科学基金会;

关键词：

Bellman's equations; Finite differences; Fully nonlinear parabolic equations; VISCOSITY SOLUTIONS; REGULARITY THEORY; INTERIOR;

D O I：

10.1080/03605302.2012.756013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1038 / 1068

页数：31

共 23 条

[1]

[Anonymous], 1996, 2 ORDER PARABOLIC DI, DOI DOI 10.1142/3302

[2]

[Anonymous], 1996, Progress in Elliptic and Parabolic Partial Differential Equations (Capri, 1994), Pitman Res. Notes Math. Ser.

[3] Interior C2,α regularity theory for a class of nonconvex fully nonlinear elliptic equations [J].