17 citations · 29 across the 22 of their papers we have counts for
29 papers
Geometric Hardy inequalities on the Heisenberg groups via convexity
Gerassimos Barbatis, Marianna Chatzakou, Achilles Tertikas
We prove -Hardy inequalities with distance to the boundary for domains in the Heisenberg group , . Our results are based on a certain geometric condit…
Sobolev improvements on sharp Rellich inequalities
Gerassimos Barbatis, Achilles Tertikas
There are two Rellich inequalities for the bilaplacian, that is for , the one involving and the other involving at the RHS. In this article we con…
The Hardy constant: a review
Gerassimos Barbatis
We present a review of results that have been obtained in the past twenty-five years concerning the -Hardy inequality with distance to the boundary. We concentrate on results…
Heat and Martin kernel estimates for Schrödinger operators with critical Hardy potentials
Gerassimos Barbatis, Konstantinos T. Gkikas, Achilles Tertikas
Let be a bounded domain in with boundary and let be either a submanifold of the boundary of codimension or a point. In this…
Finsler-Rellich inequalities involving the distance to the boundary
Gerassimos Barbatis, Miltiadis Paschalis
We study Rellich inequalities associated to higher-order elliptic operators in the Euclidean space. The inequalities are expressed in terms of an associated Finsler metric. In the…
Heat kernel estimates for fourth order non-uniformly elliptic operators with non strongly convex symbols
Gerassimos Barbatis, Panagiotis Branikas
We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols…