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arXiv · 1208.4373

On the existence of smooth solutions for fully nonlinear parabolic equations with measurable "coefficients" without convexity assumptions

Hongjie Dong·Nicolai V. Krylov
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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.

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Hongjie Dong, Nicolai V. Krylov. 2012-08-21. On the existence of smooth solutions for fully nonlinear parabolic equations with measurable "coefficients" without convexity assumptions. https://arxiv.org/abs/1208.4373

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