Boundary Riesz potential estimates for parabolic equations with measurable nonlinearities - Ho-Sik Lee; Youchan Kim (Communications in Analysis and Mechanics)
We obtain a boundary pointwise gradient estimate on a parabolic half cube $ Q_{2R} \cap \{ (x^{1}, x', t) \in \mathbb{R}^{n+1} : x^{1} > 0 \} $ for nonlinear parabolic equations with measurable nonlinearities, which are only assumed to be measurable in $ x^{1} $-variable. The estimates are obtained in terms of Riesz potential of the right-hand side measure and the oscillation of the boundary data, where the boundary data is given on $ Q_{2R} \cap \{ (x^{1}, x', t) \in \mathbb{R}^{n+1} : x^{1} = 0 \} $.