10 papers
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 -Laplacian equation \[ u_t = Δu + (p-2)|\nabla u|^{-2}\nabla^2u(\…
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…
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…
Absence of spectrum for asymptotically flat diffusions in region with cavities
Agnid Banerjee, Nicola Garofalo
We study solutions to variable-coefficient elliptic equations of the form $-\D(A(x) \nabla u) = κu$, , in an exterior domain $\Om\subset \Rn$, where is uniformly ellipt…
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 , for . Our main result, Theorem 1.1, establishes a…
Schrödinger semigroups and the Hörmander hypoellipticity condition
Nicola Garofalo, Alessandra Lunardi
We introduce a class of (possibly) degenerate dispersive equations with a drift. We prove that, under the Hörmander hypoellipticity condition, the relevant Cauchy problem can be un…
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…
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 , there exist no nontrivial solution of the Helmholtz equat…
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.
Non-divergence form parabolic equations associated with non-commuting vector fields: Boundary behavior of nonnegative solutions
M. Frentz, N. Garofalo, E. Götmark +2
In a cylinder we study the boundary behavior of nonnegative solutions of second order parabolic equations of the form \[ Hu =\sum_{i,j=1}^ma_{…