Xiaolong Li
Published 2020-06-30Version 1
We prove that the moduli of continuity of viscosity solutions to fully nonlinear parabolic partial differential equations are viscosity subsolutions of suitable parabolic equations of one space variable. As applications, we obtain sharp Lipschitz bounds and gradient estimates for fully nonlinear parabolic equations with bounded initial data, via comparison with one-dimensional solutions. This work extends multiple results of Andrews and Clutterbuck for quasilinear equations to fully nonlinear equations.
Comments: comments are welcome, 20 pages
Fully nonlinear parabolic equations in two space variables
An ersatz existence theorem for fully nonlinear parabolic equations without convexity assumptions
On the existence of $W^{1,2}_{p}$ solutions for fully nonlinear parabolic equations under either relaxed or no convexity assumptions
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