Abstract
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.
Original language | English (US) |
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Pages (from-to) | 1038-1068 |
Number of pages | 31 |
Journal | Communications in Partial Differential Equations |
Volume | 38 |
Issue number | 6 |
DOIs | |
State | Published - Jun 1 2013 |
Keywords
- Bellman's equations
- Finite differences
- Fully nonlinear parabolic equations