3 papers
math.AP2026
Fractional operators and Sobolev spaces on homogeneous groups
Nicola Garofalo, Annunziata Loiudice, Dimiter Vassilev
We establish foundational properties of fractional operators on Lie groups of homogeneous type. We prove embedding theorems for the associated Sobolev-type spaces.
math.AP2025
Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
Somnath Gandal, Annunziata Loiudice, Jagmohan Tyagi
We study the following class of quasilinear degenerate elliptic equations with critical nonlinearity \begin{align*} \begin{cases}-Δ_{γ,p} u= λ|u|^{q-2}u+|u|^{p_γ^{*}-2}u & \text{ i…
math.AP2022
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 $\frlap$…