Vedansh Arya

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20202026

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Showing 2022Show all

4 papers · 1 filter

math.AP2022

Space-like quantitative uniqueness for parabolic operators

Vedansh Arya, Agnid Banerjee

We obtain sharp maximal vanishing order at a given time level for solutions to parabolic equations with a $C^{1}$ potential $V$ . Our main result Theorem 1.1 is a parabolic generali…

math.AP2022

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 $G$ for functions satisfying the discrepancy assumption in…

math.AP2022

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 $(\partial_{t} - Δ)^{s} u = V u$ for $s \in [1/2, 1)$ via new Carleman estimates. Our main r…

math.AP2022

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 $(\partial_{t} - Δ)^{s} u = V u$ , for $0 < s < 1$ . The proof of our main resul…