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math.AP2021
Borderline gradient continuity for fractional heat type operators
Vedansh Arya, Dharmendra Kumar
In this paper, we establish gradient continuity for solutions to \[ (\partial_t - \operatorname{div}(A(x) \nabla u))^s =f,\ s \in (1/2, 1), \] when belongs to the scaling criti…
math.AP2021
Boundary differentiability of solutions to elliptic equations in convex domains in the borderline case
Dharmendra Kumar
In this work, we consider the following elliptic partial differential equations: \begin{equation*} \left\{ \begin{aligned}{} - b_{ij} \; \frac{\partial^{2} w}{\partial x_{i} \parti…