13 papers
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…
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 to nondivergence form operators. We prove an intrinsic Harnack ineq…
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…
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…
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…
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 coefficients and inhomogeneity, where with $n…