Research
My research area is in the intersection of Harmonic Analysis, PDE, applied math in particular traffic flow model. More specifically I study elliptic and parabolic PDEs in the nonlocal setting. To know more about my research please go through my publications.
List of Publications (Accepted / Submitted):
Publications (Accepted):
1. Harnack inequalities and H\"older estimates for master equations, accepted in SIAM J. Math. Anal. (2021) (with M. De Le\'on-Contreras and P. R. Stinga).
2. Regularity estimates for nonlocal space-time master equations in bounded domains , accepted in J. Evol. Equ. (2020) (with P. R. Stinga) .
3. Nonlocal Calculus-based Macroscopic Traffic Model: Development, Analysis, and Validation, accepted in IEEE OJ-ITS, (2023), (with P. Kachroo, S. Agarwal, A. J. Huang).
4. Sharp extension problem characterizations for higher fractional power operators in Banach spaces, accepted in J. Funct. Anal. (2024) (with P. R. Stinga).
5. Incorporating Nonlocal Traffic Flow Model in Physics informed Neural Networks, accepted in IEEE TITS (2024), (with A. J. Huang, S. Agarwal).
(Preprint):
6. Nonlocal mean curvature problems for integrable interaction kernels, (2022) (with M. Foss, P. Radu), arXiv:2212.01530 .