Agnid Banerjee

activity

20122026

most citedSome local properties of subsolutons and supersolutions for a doubly nonlinear nonlocal parabolic

p

-Laplace equation

4 citations · 10 across the 43 of their papers we have counts for

collaborators

53 papers

math.AP2026

A nonlinear Li-Yau inequality and its consequences

Agnid Banerjee, Nicola Garofalo, Hamidreza Mahmoudian

We prove a sharp nonlinear analogue of the Li-Yau inequality for positive solutions of the normalized parabolic $p$ -Laplacian equation \[ u_t = Δu + (p-2)|\nabla u|^{-2}\nabla^2u(\…

math.AP2026

Quantitative uniqueness for parabolic equations with Hölder potentials

Agnid Banerjee, Nicola Garofalo

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 Bour…

math.AP2026

A strong unique continuation result for the Baouendi operator

Agnid Banerjee, Nicola Garofalo

We establish a strong unique continuation property for the subelliptic Baouendi operator under the presence of zero-order perturbations satisfying an almost Hardy-type growth condi…

math.AP2025

Absence of $L^{p}$ spectrum for asymptotically flat diffusions in region with cavities

Agnid Banerjee, Nicola Garofalo

We study solutions to variable-coefficient elliptic equations of the form $-\D(A(x) \nabla u) = κu$, $κ > 0$ , in an exterior domain $\Om\subset \Rn$, where $A (x)$ is uniformly ellipt…

math.AP2024

On unique continuation in measure for fractional heat equations

Agnid Banerjee, Nicola Garofalo

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 $0 < s < 1$ . Our main result, Theorem 1.1, establishes a…

math.AP2024

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…

math.AP2023

An observation on eigenfunctions of the Laplacian

Agnid Banerjee, Nicola Garofalo

In his seminal 1943 paper F. Rellich proved that, in the complement of a cavity $Ω = {x \in R^{n} ∣ ∣ x ∣ > R_{0}}$ , there exist no nontrivial solution $f$ of the Helmholtz equat…

math.AP2023

A Rellich type estimate for a subelliptic Helmholtz equation with mixed homogeneities

Agnid Banerjee, Nicola Garofalo

We establish an optimal asymptotic on rings for a subelliptic Helmholtz equation with mixed homogeneities.

math.AP2023

Decay at infinity for solutions to some fractional parabolic equations

Agnid Banerjee, Abhishek Ghosh

For $s \in [1/2, 1)$ , let $u$ solve $(\partial_{t} - Δ)^{s} u = V u$ in $R^{n} \times [- T, 0]$ for some $T > 0$ where $∣∣ V ∣ ∣_{C^{2} (R^{n} \times [- T, 0])} < \infty$ . We show…

math.AP2023

Sharp asymptotic of solutions to some nonlocal parabolic equations

Agnid Banerjee, Abhishek Ghosh

We show that if $u$ solves the fractional parabolic equation $(\partial_{t} - Δ)^{s} u = V u$ in $B_{5} \times (- 25, 0]$ ( $0 < s < 1$ ) such that $u (\cdot, 0) \neq \equiv 0$ , then the maximal v…

math.AP2023

On the forward in time propagation of zeros in fractional heat type problems

Agnid Banerjee, Nicola Garofalo

In this short note we prove that if $u$ solves $(\partial_{t} - Δ)^{s} u = V u$ in $R_{x}^{n} \times R_{t}$ , and vanishes to infinite order at a point $(x_{0}, t_{0})$ , then $u \e…

math.AP2022

Borderline gradient continuity for the normalized $p$ -parabolic operator

Murat Akman, Agnid Banerjee, Isidro H. Munive

In this paper, we prove gradient continuity estimates for viscosity solutions to $Δ_{p}^{N} u - u_{t} = f$ in terms of the scaling critical $L (n + 2, 1)$ norm of $f$ , where $Δ_{p}^{N}$ is th…

math.AP2022

Higher order Boundary Schauder Estimates in Carnot Groups

Agnid Banerjee, Nicola Garofalo, Isidro H. Munive

In his seminal 1981 study D. Jerison showed the remarkable negative phenomenon that there exist, in general, no Schauder estimates near the characteristic boundary in the Heisenber…

math.AP2022

Extension problem for the fractional parabolic Lamé operator and unique continuation

Agnid Banerjee, Soumen Senapati

In this paper, we introduce and analyse an explicit formulation of fractional powers of the parabolic Lamé operator $H$ and we then study the extension problem associated…

math.AP2022

Space-like quantitative uniqueness for parabolic operators

Vedansh Arya, Agnid Banerjee

We obtain sharp maximal vanishing order at a given time level for solutions to parabolic equations with a $C^{1}$ potential $V$ . Our main result Theorem 1.1 is a parabolic generali…

math.AP2022

Strong unique continuation for variable coefficient parabolic operators with Hardy type potential

Agnid Banerjee, Pritam Ganguly, Abhishek Ghosh

In this paper, we prove the strong unique continuation property at the origin for solutions of the following scaling critical parabolic differential inequality \[ |\operatorname{di…

math.AP2022

The Calderón problem for space-time fractional parabolic operators with variable coefficients

Agnid Banerjee, Soumen Senapati

We study an inverse problem for variable coefficient fractional parabolic operators of the form $(\partial_{t} - div (A (x) \nabla_{x})^{s} + q (x, t)$ for $s \in (0, 1)$ and show…

math.AP2022

On the space-like analyticity in the extension problem for nonlocal parabolic equations

Agnid Banerjee, Nicola Garofalo

In this note we give an elementary proof of the space-like real analyticity of solutions to a degenerate evolution problem that arises in the study of fractional parabolic operator…

math.AP2022

Quantitative uniqueness for fractional heat type operators

Vedansh Arya, Agnid Banerjee

In this paper we obtain quantitative bounds on the maximal order of vanishing for solutions to $(\partial_{t} - Δ)^{s} u = V u$ for $s \in [1/2, 1)$ via new Carleman estimates. Our main r…

math.AP2022

Space-like strong unique continuation for some fractional parabolic equations

Vedansh Arya, Agnid Banerjee, Donatella Danielli +1

In this paper we establish the \emph{space-like} strong unique continuation for nonlocal equations of the type $(\partial_{t} - Δ)^{s} u = V u$ , for $0 < s < 1$ . The proof of our main resul…

math.AP2021

Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic $p$ -Laplace equations

Agnid Banerjee, Prashanta Garain, Juha Kinnunen

We discuss pointwise behavior of weak supersolutions for a class of doubly nonlinear parabolic fractional $p$ -Laplace equations which includes the fractional parabolic $p$ -Laplace…

math.AP2020

Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation

Agnid Banerjee, Ramesh Manna

In this paper, we obtain new Carleman estimates for a class of variable coefficient degenerate elliptic operators whose constant coefficient model at one point is the so called Bao…

math.AP2020★ 4 cited

Some local properties of subsolutons and supersolutions for a doubly nonlinear nonlocal parabolic $p$ -Laplace equation

Agnid Banerjee, Prashanta Garain, Juha Kinnunen

We establish a local boundedness estimate for weak subsolutions to a doubly nonlinear parabolic fractional $p$ -Laplace equation. Our argument relies on energy estimates and a parab…

math.AP2020

Unified approach to $C^{1, α}$ regularity for quasilinear parabolic equations

Karthik Adimurthi, Agnid Banerjee

In this paper, we are interested in obtaining a unified approach for $C^{1, α}$ estimates for weak solutions of quasilinear parabolic equations, the prototype example being \[ u_t -…

A nonlinear Li-Yau inequality and its consequences

Quantitative uniqueness for parabolic equations with Hölder potentials

A strong unique continuation result for the Baouendi operator

Absence of Lp spectrum for asymptotically flat diffusions in region with cavities

On unique continuation in measure for fractional heat equations

Sharp order of vanishing for parabolic equations, nodal set estimates and Landis type results

An observation on eigenfunctions of the Laplacian

A Rellich type estimate for a subelliptic Helmholtz equation with mixed homogeneities

Decay at infinity for solutions to some fractional parabolic equations

Sharp asymptotic of solutions to some nonlocal parabolic equations

On the forward in time propagation of zeros in fractional heat type problems

Borderline gradient continuity for the normalized p-parabolic operator

Higher order Boundary Schauder Estimates in Carnot Groups

Extension problem for the fractional parabolic Lamé operator and unique continuation

Space-like quantitative uniqueness for parabolic operators

Strong unique continuation for variable coefficient parabolic operators with Hardy type potential

The Calderón problem for space-time fractional parabolic operators with variable coefficients

On the space-like analyticity in the extension problem for nonlocal parabolic equations

Quantitative uniqueness for fractional heat type operators

Space-like strong unique continuation for some fractional parabolic equations

Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic p-Laplace equations

Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation

Some local properties of subsolutons and supersolutions for a doubly nonlinear nonlocal parabolic p-Laplace equation

Unified approach to C1,α regularity for quasilinear parabolic equations

Absence of $L^{p}$ spectrum for asymptotically flat diffusions in region with cavities

Borderline gradient continuity for the normalized $p$ -parabolic operator

Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic $p$ -Laplace equations

Some local properties of subsolutons and supersolutions for a doubly nonlinear nonlocal parabolic $p$ -Laplace equation

Unified approach to $C^{1, α}$ regularity for quasilinear parabolic equations