Dr Vivek Tewary, Assistant Professor, Mathematics, SIAS presented a research talk on Regularity theory for nonlocal p-Laplace equations at GANIT Symposium on Stochastic Processes and Related Topics 2025 held at IIT Gandhinagar from 13-15 September 2025.
About the talk: Brownian motion is related to the Laplace operator as jump Levy processes are related to the nonlocal Laplace operator. Similarly, the p-Laplace operator has a probabilistic interpretation in a tug-of-war game with noise and the nonlocal p-Laplace operator comes from a nonlocal version of this tug-of-war game. A recent turn is to study these operators using non-probabilistic methods. While the probabilistic interpretations are linked to non-divergence type operators, in this talk, we focus on one of their divergence type counterparts. In particular, we discuss the local boundedness and local Holder regularity of solutions of the parabolic divergence type nonlocal p-Laplace equation.
About the workshop: The aim of this meet is to bring together researchers in the country working on stochastic processes and related areas (such as partial differential equations, dynamical systems) for a series of stimulating lectures and discussions. It is hoped that this can be the first meet in an annual tradition and provide a forum for explorations of new ideas and forging of new collaborations.
