59 citations · 125 across the 23 of their papers we have counts for
26 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…
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…
Best Sobolev constants in the presence of sharp Hardy terms in Euclidean and hyperbolic space
Gerassimos Barbatis, Achilles Tertikas
In this article we compute the best Sobolev constants for various Hardy-Sobolev inequalities with sharp Hardy term. This is carried out in three different environments: interior po…
Sharp Hardy and Hardy--Sobolev inequalities with point singularities on the boundary
Gerassimos Barbatis, Stathis Filippas, Achilles Tertikas
We study the Hardy inequality when the singularity is placed on the boundary of a bounded domain in that satisfies both an interior and exterior ball condition at th…
Rigidity results with applications to best constants and symmetry of Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities
Jean Dolbeault, Maria J. Esteban, Stathis Filippas +1
We take advantage of a rigidity result for the equation satisfied by an extremal function associated with a special case of the Caffarelli-Kohn-Nirenberg inequalities to get a symm…