Weighted Lp(⋅) -regularity for fully nonlinear parabolic equations
We prove a global weighted Lp(⋅) -regularity for the Hessian of strong solution to the Cauchy–Dirichlet problem for fully nonlinear parabolic equations in a bounded C1,1 -domain, where the associated nonlinearity is (δ,R) -vanishing in independent variables, the variable exponent p(⋅) is log -Hölder continuous, and the weight ω is of the Ap(⋅)/(n+1) class. As a consequence, we also derive Morrey’s regularity for the Hessian of strong solution to this problem under consideration, which implies a global Hölder continuity of the spatial gradient under the assumption of higher regular datum.
Zhang, J., Zheng, S. & Feng, Z. Weighted Lp(⋅) -regularity for fully nonlinear parabolic equations. Calc. Var. 59, 190 (2020). https://doi.org/10.1007/s00526-020-01848-9