Agnid Banerjee

About

Agnid Banerjee is an associate professor in the School of Mathematical and Statistical Sciences at Arizona State University. His research is focused on the field of elliptic and parabolic partial differential equations and their analysis. His work primarily addresses questions related to regularity, unique continuation, potential theory, and free boundary problems. Prior to joining ASU, Banerjee was an associate professor at the Tata Institute of Fundamental Research in India. He earned his PhD in Mathematics from Purdue University in 2014 and holds a bachelor's degree in Mathematics and Computer Science from Chennai Mathematical Institute, India, completed in 2008.

Research topics

• Mathematics
• Applied mathematics
• Physics
• Mathematical analysis

Selected publications

• The Calderón Problem for Space-Time Fractional Parabolic Operators with Variable Coefficients

  SIAM Journal on Mathematical Analysis · 2024-07-03 · 7 citations

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• Sharp asymptotic of solutions to some nonlocal parabolic equations

  Discrete and Continuous Dynamical Systems · 2024-10-11 · 1 citations

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  We show that if $ u $ solves the fractional parabolic equation $ (\partial_t - \Delta )^s u = Vu $ in $ B_5 \times (-25, 0] $ ($ 0<s<1 $) such that $ u(\cdot, 0) \not\equiv 0 $, then the maximal vanishing order of $ u $ in space-time at $ (0, 0) $ is upper bounded by $ C\left(1+\|V\|_{C^{1}_{(x, t)}}^{1/2s}\right) $. As $ s \to 1 $, it converges to the sharp maximal order of vanishing due to Donnelly-Fefferman and Bakri. This quantifies a space-like strong unique continuation result recent…

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• Extension problem for the fractional parabolic Lamé operator and unique continuation

  Calculus of Variations and Partial Differential Equations · 2024-08-20 · 1 citations

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• Quantitative uniqueness for parabolic equations with Hölder potentials

  ArXiv.org · 2026-04-14

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  In this note we derive a space-like quantitative uniqueness result for parabolic operators with Hölder zero-order term that interpolates between the Donnelly-Fefferman and the Bourgain-Kenig estimate. This generalizes a recent result of Teng, Wang and Zhu for the time-independent Schrödinger operator with a Hölder potential.

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• On unique continuation in measure for fractional heat equations

  Proceedings of the American Mathematical Society · 2026-04-24

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  We prove a theorem of unique continuation in measure for nonlocal equations of the type $(\partial_t - Δ)^s u= V(x,t) u$, for $0

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Frequent coauthors

• Nicola Garofalo

  56 shared

• Isidro H. Munive

  13 shared

• Ramesh Manna

  Homi Bhabha National Institute

  12 shared

• Vedansh Arya

  10 shared

• Karthik Adimurthi

  9 shared

• Abhishek Ghosh

  7 shared

• Donatella Danielli

  7 shared

• Ram Baran Verma

  6 shared

Education

• Ph.D.

  Purdue University

  2014

• B.S., Mathematics and Computer Science

  Chennai Mathematical Institute, India

  2008

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