Vedansh Arya

activity

20202026

collaborators

13 papers

math.AP2026

Eventual regularity of the volume-preserving mean curvature flow in three and two dimensions

Vedansh Arya, Seongmin Jeon, Vesa Julin

The recent work of Morini-Oronzio-Spadaro and the third author shows that, in three dimensions, a flat-flow solution of the volume-preserving mean curvature flow that converges to…

math.AP2025

Harnack inequality for degenerate fully nonlinear parabolic equations

Vedansh Arya, Vesa Julin

We consider degenerate fully nonlinear parabolic equations, which generalize the p-parabolic equation with $p > 2$ to nondivergence form operators. We prove an intrinsic Harnack ineq…

math.DG2025

The asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus

Vedansh Arya, Daniele De Gennaro, Anna Kubin

We study the asymptotic behavior of flat flow solutions to the periodic and planar two-phase Mullins-Sekerka flow and area-preserving curvature flow. We show that flat flows conver…

math.AP2024

Sharp order of vanishing for parabolic equations, nodal set estimates and Landis type results

Vedansh Arya, Agnid Banerjee, Nicola Garofalo

We establish a new sharp estimate of the order of vanishing of solutions to parabolic equations with variable coefficients. For real-analytic leading coefficients, we prove a local…

math.AP2024

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…

math.AP2024

Optimal regularity for the variable coefficients parabolic Signorini problem

Vedansh Arya, Wenhui Shi

In this paper we discuss the optimal regularity of the variable coefficient parabolic Signorini problem with $W_{p}^{1, 1}$ coefficients and $L^{p}$ inhomogeneity, where $p > n + 2$ with $n…

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…

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 $f$ 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…

math.AP2020

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…