79 citations · 327 across the 58 of their papers we have counts for
6 papers · 2 filters
Optimal decay for solutions of nonlocal semilinear equations with critical exponent in homogeneous group
Nicola Garofalo, Annunziata Loiudice, Dimiter Vassilev
In this paper we establish the sharp asymptotic decay of positive solutions of the Yamabe type equation $\frlap u=u^{\frac{Q+2s}{Q-2s}}$ in a homogeneous Lie group, where $\frlap$…
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…
A universal heat semigroup characterisation of Sobolev and BV spaces in Carnot groups
Nicola Garofalo, Giulio Tralli
In sub-Riemannian geometry there exist, in general, no known explicit representations of the heat kernels, and these functions fail to have any symmetry whatsoever. In particular,…
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…
A note on monotonicity and Bochner formulas in Carnot groups
Nicola Garofalo
In this note we prove two monotonicity formulas for solutions of and $Δ_H f - \p_t f = c$ in Carnot groups. Such formulas involve the right-invariant \emph{carré du cha…
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 , for . The proof of our main resul…