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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
An Intrinsic Harnack inequality for some non-homogeneous parabolic equations in non-divergence form
Vedansh Arya
In this paper, we establish a scale invariant Harnack inequality for some inhomogeneous parabolic equations in a suitable intrinsic geometry dictated by the nonlinearity. The class…