Paper Info
Title
An Ersatz Existence Theorem for Fully Nonlinear Parabolic Equations without Convexity Assumptions.
Abstract
We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in the whole space or in any cylindrical smooth domain with smooth boundary data one can find an approximating equation which has a continuous solution with the first and the second spatial derivatives under control: bounded in the case of the whole space and locally bounded in the case of equations in cylinders. The approximating equation is constructed in such a way that it modifies the original one only for large values of the second spatial derivatives of the unknown function. This is different from a previous work of Hongjie Dong and the author, where the modification was done for large values of the unknown function and its spatial derivatives.
Year
DOI
Venue
2013
10.1137/120903762
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
fully nonlinear equations,parabolic equations,Bellman's equations,finite differences
Existence theorem,Parabolic partial differential equation,Mathematical optimization,Convexity,Nonlinear system,Mathematical analysis,Finite difference,Mathematics,Independent equation,Parabola,Bounded function
Journal
Volume
Issue
ISSN
45
6
0036-1410
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
N. V. Krylov1511.53