8 papers · 1 filter
Asymptotics and Scattering for Critically Weakly Hyperbolic and Singular Systems
Bolys Sabitbek, Arick Shao
We study a very general class of first-order linear hyperbolic systems that both become weakly hyperbolic and contain lower-order coefficients that blow up at a single time …
Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, III: singular coefficients
Claudia Garetto, Bolys Sabitbek
In this paper we continue the analysis of non-diagonalisable hyperbolic systems initiated in \cite{GarJRuz, GarJRuz2}. Here we assume that the system has discontinuous coefficients…
Geometric Hardy inequalities on starshaped sets
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, we present the geometric Hardy inequalities on the starshaped sets in the Carnot groups. Also, we obtain the geometric Hardy inequalities on half-spaces for general…
Geometric Hardy and Hardy-Sobolev inequalities on Heisenberg groups
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, we present the geometric Hardy inequality for the sub-Laplacian in the half-spaces on the stratified groups. As a consequence, we obtain the following geometric Hard…
Weighted anisotropic Hardy and Rellich type inequalities for general vector fields
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, we establish the weighted anisotropic Hardy and Rellich type inequalities with boundary terms for general (real-valued) vector fields. As consequences, we derive new…
Subelliptic geometric Hardy type inequalities on half-spaces and convex domains
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper we present and versions of the geometric Hardy inequalities in half-spaces and convex domains on stratified (Lie) groups. As a consequence, we obtain the…