1 citations · 5 across the 25 of their papers we have counts for
13 papers · 2 filters
Higher order hypoelliptic damped wave equations on graded Lie groups with data from negative order Sobolev spaces: the critical case
Vishvesh Kumar, Shyam Swarup Mondal, Michael Ruzhansky +1
Let be a graded Lie group with homogeneous dimension . In this paper, we study the Cauchy problem for a semilinear hypoelliptic damped wave equation involving a posi…
Subelliptic Nonlocal Brezis-Nirenberg Problems on Stratified Lie Groups
Sekhar Ghosh, Vishvesh Kumar, Michael Ruzhansky
In this paper, we investigate the subelliptic nonlocal Brezis-Nirenberg problem on stratified Lie groups involving critical nonlinearities, namely, \begin{align*} (-Δ_{\mathbb{G},…
Nuclearity, Schatten-von Neumann classes, distribution of eigenvalues and --boundedness of Fourier integral operators on compact manifolds
Duván Cardona, Julio Delgado, Michael Ruzhansky
We link Sogge's type -estimates for eigenfunctions of the Laplacian on compact manifolds with the problem of providing criteria for the -nuclearity of Fourier integral oper…
On fractional inequalities on metric measure spaces with polar decomposition
Aidyn Kassymov, Michael Ruzhansky, Gulnur Zaur
In this paper, we prove the fractional Hardy inequality on polarisable metric measure spaces. The integral Hardy inequality for is playing a key role in the proo…
Nearness and solvability of non-invariant equations on stratified groups
Marianna Chatzakou, Michael Ruzhansky, Nikos Yannakakis
We prove the well-posedness of the differential equation in the setting of a stratified group when the considered second-order differential operator can be…
Well-posedness for a class of pseudo-differential hyperbolic equations on the torus
Duvan Cardona, Julio Delgado, Michael Ruzhansky
In this paper we establish the well-posedness of the Cauchy problem for a class of pseudo-differential hyperbolic equations on the torus. The class considered here includes a space…
Higher order hypoelliptic damped wave equations on graded Lie groups with data from negative order Sobolev spaces
Aparajita Dasgupta, Vishvesh Kumar, Shyam Swarup Mondal +1
Let be a graded Lie group with homogeneous dimension . In this paper, we study the Cauchy problem for a semilinear hypoelliptic damped wave equation involving a posi…
On global solutions of heat equations with time-dependent nonlinearities on unimodular Lie groups
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this work, we study the global well-posedeness of the heat equation with variable time-dependent nonlinearity of the form on unimodular Lie groups when the differenti…
-bounds in Safarov pseudo-differential calculus on manifolds with bounded geometry
Santiago Gómez Cobos, Michael Ruzhansky
Given a smooth complete Riemannian manifold with bounded geometry and a linear connection on it (not necessarily a metric one), we prove the -boundedness of o…
Pseudo-differential operators on Homogeneous vector bundles over compact homogeneous manifolds
Duván Cardona, Vishvesh Kumar, Michael Ruzhansky
In this work, we introduce a global theory of subelliptic pseudo-differential operators on arbitrary homogeneous vector bundles over orientable compact homogeneous manifolds. We wi…
The weak (1,1) boundedness of Fourier integral operators with complex phases
Duván Cardona, Michael Ruzhansky
Let be a Fourier integral operator of order associated with a canonical relation locally parametrised by a real-phase function. A fundamental result due to Seeger, S…
Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations
Duván Cardona, Marianna Chatzakou, Julio Delgado +2
In this work we consider the semigroup for associated to an anharmonic oscillator of the form …
Semilinear damped wave equations on the Heisenberg group with initial data from Sobolev spaces of negative order
Aparajita Dasgupta, Vishvesh Kumar, Shyam Swarup Mondal +1
In this paper, we focus on studying the Cauchy problem for semilinear damped wave equations involving the sub-Laplacian on the Heisenberg group with po…