9 papers
A nonlinear Li-Yau inequality and its consequences
Agnid Banerjee, Nicola Garofalo, Hamidreza Mahmoudian
We prove a sharp nonlinear version of the celebrated Li-Yau inequality for positive solutions of the normalized parabolic -Laplacian equation $u_t = Δu + (p-2)|\nabla u|^{-2}\na…
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…