C^{1, α}-regularity for solutions of degenerate/singular fully nonlinear parabolic equations

2023/03/16 by Lee, Ki-Ahm, Lee, Se-Chan, Yun, Hyungsung
#35B65 #35D40 #35K20 #35K65 #35K67 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.09059

Abstract

We establish the interior C^1,α-estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations u_t = |Du|^γF(D²u) + f. For this purpose, we prove the well-posedness of the regularized Dirichlet problem \ \beginaligned u_tamp;=(1+|Du|²)^γ/2F(D²u) amp;amp;in Q₁ \newline uamp;=φamp;amp;on ∂_p Q₁. \endaligned. Our approach utilizes the Bernstein method with approximations in view of difference quotient.

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