79 citations · 327 across the 58 of their papers we have counts for
9 papers · 1 filter
A heat equation approach to intertwining
Nicola Garofalo, Giulio Tralli
In this paper we present a new approach based on the heat equation and extension problems to some intertwining formulas arising in conformal CR geometry.
The thin obstacle problem for some variable coefficient degenerate elliptic operators
Agnid Banerjee, Federico Buseghin, Nicola Garofalo
In this paper we establish the optimal interior regularity and the smoothness of the regular part of the free boundary in the thin obstacle problem for a class of degener…
Heat kernels for a class of hybrid evolution equations
Nicola Garofalo, Giulio Tralli
The aim of this paper is to construct (explicit) heat kernels for some hybrid evolution equations which arise in physics, conformal geometry and subelliptic PDEs. Hybrid means that…
Feeling the heat in a group of Heisenberg type
Nicola Garofalo, Giulio Tralli
In this paper we use the heat equation in a group of Heisenberg type to provide a unified treatment of the two very different extension problems for the time independe…
A Bourgain-Brezis-Mironescu-Dávila theorem in Carnot groups of step two
Nicola Garofalo, Giulio Tralli
In this note we prove the following theorem in any Carnot group of step two : \[ \underset{s\nearrow 1/2}{\lim} (1 - 2s) \mathfrak P_{H,s}(E) = \frac{4}{\sqrt π}\ \math…
A strong unique continuation property for the heat operator with Hardy type potential
Agnid Banerjee, Nicola Garofalo, Ramesh Manna
In this note we prove the strong unique continuation property at the origin for the solutions of the parabolic differential inequality \[ |Δu - u_t| \leq \frac{M}{|x|^2} |u|, \] wi…