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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 , for . Our main result, Theorem 1.1, establishes a…
math.AP2024
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…
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…