Speaker: Vedansh Arya (University of Jyväskylä)
Date and Time: Wednesday, January 8, 2025, at 4:15 PM
Venue: Ramanujan Hall
Title: Harnack Estimate for Non-Homogeneous Parabolic Equations
Abstract: In this talk, we present a scale-invariant Harnack inequality
for certain non-homogeneous parabolic equations within a suitable
intrinsic geometry influenced by the nonlinearity. This result, in
particular, establishes Hölder continuity. Additionally, we discuss a
Harnack-type estimate on a global scale that provides a quantitative
formulation of the strong minimum principle. The talk is based on joint
work with Vesa Julin.
Speaker Bio: Vedansh Arya has been a postdoctoral researcher in the
Department of Mathematics and Statistics at the University of Jyväskylä,
Finland, since 2022. He completed his Ph.D. in Mathematics at the TIFR
Centre for Applicable Mathematics, Bangalore, in the same year. His
research interests span regularity theory for elliptic and parabolic PDEs,
unique continuation problems, free boundary problems, and mean curvature
flow.