49 citations · 113 across the 27 of their papers we have counts for
29 papers
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.
Overdetermined fractional Serrin problem
Nicola Garofalo, Dimiter Vassilev
We solve a version of the Serrin overdetermined problem for the Weinstein operator involving a Bessel operator.
Overdetermined problems in groups of Heisenberg type: conjectures and partial results
Nicola Garofalo, Dimiter Vassilev
In this paper we formulate some conjectures in sub-Riemannian geometry concerning a characterisation of the Koranyi-Kaplan ball in a group of Heisenberg type through the existence…
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 $\frlap$…
Corrigenda to " estimates and asymptotic behavior for finite energy solutions of extremals to Hardy-Sobolev inequalities", Trans. Amer. Math. Soc. 363 (2011), no. 1, 37--62
Dimiter Vassilev
Corrigenda to " estimates and asymptotic behavior for finite energy solutions of extremals to Hardy-Sobolev inequalities", Trans. Amer. Math. Soc. 363 (2011), no. 1, 37--62.
The Obata first eigenvalue theorems on a seven dimensional quaternionic contact manifold
Abdelrahman Mohamed, Dimiter Vassilev
We show that a compact quaternionic contact manifold of dimension seven that satisfies a Lichnerowicz-type lower Ricci-type bound and has the -function of any eigenfunction of t…