C1,α-regularity for solutions of degenerate/singular fully nonlinear parabolic equations

Abstract

We establish the interior C1,α-estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equationsut=|Du|γF(D2u)+fin Q1, where γ>−1 and f∈C(Q1)∩L∞(Q1). For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem{ut=(1+|Du|2)γ/2F(D2u)in Q1u=φon ∂pQ1, where γ>−2. Our approach utilizes the Bernstein method with approximations in view of the difference quotient.