5 papers
Fujita exponent for heat equation with Hörmander vector fields
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper, we show global existence and non-existence results for the heat equation with some of the squares of smooth vector fields on $\Rn$ satisfying Hörmander's rank condit…
Zero modes and Dirac-(logarithmic) Sobolev-type inequalities
Marianna Chatzakou, Uwe Kahler, Michael Ruzhansky
We study the decay rate of the zero modes of the Dirac operator with a matrix-valued potential that is considered here without any regularity assumptions, compared to the existing…
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…
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…
On a class of anharmonic oscillators
Marianna Chatzakou, Julio Delgado, Michael Ruzhansky
In this work we study a class of anharmonic oscillators within the framework of the Weyl-Hörmander calculus. The anharmonic oscillators arise from several applications in mathemati…