115 citations · 1.9k across the 226 of their papers we have counts for
16 papers · 2 filters
Analytic functional calculus and Gårding inequality on graded Lie groups with applications to diffusion equations
Duván Cardona, Julio Delgado, Michael Ruzhansky
In this paper we study the Cauchy problem for diffusion equations associated to a class of strongly hypoelliptic pseudo-differential operators on graded Lie groups. To do so, we de…
The heat equation with singular potentials. II: Hypoelliptic case
Marianna Chatzakou, Michael Ruzhansky, Niyaz Tokmagambetov
In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators…
Liouville theorems for Kirchhoff-type hypoelliptic Partial Differential Equations and systems. I. Heisenberg group
Aidyn Kassymov, Michael Ruzhansky, Niyaz Tokmagambetov +1
In this paper, we show the nonexistence results for the Kirchhoff elliptic, parabolic, and hyperbolic type equations on the Heisenberg groups. Also, the pseudo-parabolic and pseudo…
Subelliptic sharp Gårding inequality on compact Lie groups
Duván Cardona, Serena Federico, Michael Ruzhansky
In this work we establish a subelliptic sharp Gårding inequality on compact Lie groups for pseudo-differential operators with symbols belonging to global subelliptic Hörmander clas…
Logarithmic Hardy-Rellich inequalities on Lie groups
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper we obtain logarithmic Hardy and Rellich inequalities on general Lie groups. In the case of graded groups, we also show their refinements using the homogeneous Sobolev…
Well-posedness of Tricomi-Gellerstedt-Keldysh-type fractional elliptic problems
Michael Ruzhansky, Berikbol T. Torebek, Batirkhan Kh. Turmetov
In this paper Tricomi-Gellerstedt-Keldysh-type fractional elliptic equations are studied. The results on the well-posedness of fractional elliptic boundary value problems are obtai…