6 papers · 1 filter
Hölder Continuity and Harnack estimate for non-homogeneous parabolic equations
Vedansh Arya, Vesa Julin
In this paper we continue the study on intrinsic Harnack inequality for non- homogeneous parabolic equations in non-divergence form initiated by the first author in [1]. We establi…
Carleman estimates for sub-Laplacians on Carnot groups
Vedansh Arya, Dharmendra Kumar
In this note, we establish a new Carleman estimate with singular weights for the sub-Laplacian on a Carnot group for functions satisfying the discrepancy assumption in…
Quantitative uniqueness for fractional heat type operators
Vedansh Arya, Agnid Banerjee
In this paper we obtain quantitative bounds on the maximal order of vanishing for solutions to for via new Carleman estimates. Our main r…
Space-like strong unique continuation for some fractional parabolic equations
Vedansh Arya, Agnid Banerjee, Donatella Danielli +1
In this paper we establish the \emph{space-like} strong unique continuation for nonlocal equations of the type , for . The proof of our main resul…
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…
Strong Backward uniqueness for sublinear parabolic equations
Vedansh Arya, Agnid Banerjee
In this paper, we establish strong backward uniqueness for solutions to sublinear parabolic equations of the type (1.1). The proof of our main result Theorem 1.1 is achieved by mea…