Related papers: Dissipation and Semigroup on $H^k_n$: Non-cutoff L…

This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming $S^{n-1}$ integrability of the angular part of the collision kernel…

We show an example of benign non-separability in an apparently separable system consisting of $n$ free non-correlated quantum particles, solitonic solutions to the nonlinear phase modification of the Schr\"{o}dinger equation proposed…

We study the linear relaxation Boltzmann equation, a simple semiclassical kinetic model. We provide a resolvent estimate for an associated non-selfadjoint operator as well as an estimate on the return to equilibrium. This is done using a…

We derive estimates in a weighted Sobolev space $W^{k,p}_{\mu}(D)$ for a homotopy operator on a bounded strictly pseudoconvex domain $D$ of $C^2$ boundary in ${\C}^n$. As a result, we show that given any $2n < p < \infty$, $k > 1$, $q \geq…

In this paper, we focus on studying the Cauchy problem for semilinear damped wave equations involving the sub-Laplacian $\mathcal{L}$ on the Heisenberg group $\mathbb{H}^n$ with power type nonlinearity $|u|^p$ and initial data taken from…

The aim of the work is to provide a stable method to get sharp bounds for Boltzmann and Landau operators in weighted Sobolev spaces and in anisotropic spaces. All the sharp bounds are given for the original Boltzmann and Landau operators.…

We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equation in a bounded domain with any of the usual physical boundary conditions: in-flow, bounce-back, specular-reflection and diffuse-reflection. When the mass, energy…

We study the hydrostatic equilibrium of multi-Weyl semimetals, a class of systems with Weyl-like quasi-particles but anisotropic dispersion relation $\omega^2 \sim k_\parallel^2 + k_\perp^{2n}$, with $n$ a possitive integer. A…

We give sufficient conditions on an operator space $E$ and on a semigroup of operators on a von Neumann algebra $M$ to obtain a bounded analytic or a $R$-analytic semigroup $(T_t \otimes Id_E)_{t \geq 0}$ on the vector valued noncommutative…

We consider the kinetic theory of a three-dimensional fluid of weakly interacting bosons in a non-equilibrium state which includes both normal fluid and a condensate. More precisely, we look at the previously postulated nonlinear…

Let $\mathcal{X}$ be a real separable Hilbert space. Let $C$ be a linear, bounded and positive operator on $\mathcal{X}$ and let $A$ be the infinitesimal generator of a strongly continuous semigroup on $\mathcal{X}$. Let $\{W(t)\}_{t\geq…

This paper deals with the long time behavior of solutions to the spatially homogeneous Boltzmann equation. The interactions considered are the so-called (non cut-off and non mollified) hard potentials. We prove an exponential in time…

We prove explicit coercivity estimates for the linearized Boltzmann and Landau operators, for a general class of interactions including any inverse-power law interactions, and hard spheres. The functional spaces of these coercivity…

We consider a discrete Schr\"odinger operator $ H_\varepsilon= -\varepsilon^2\Delta_\varepsilon + V_\varepsilon$ on $\ell^2(\varepsilon \mathbb Z^d)$, where $\varepsilon>0$ is a small parameter and the potential $V_\varepsilon$ is defined…

We study the functional calculus associated with a hypoelliptic left-invariant differential operator $\mathcal{L}$ on a connected and simply connected nilpotent Lie group $G$ with the aid of the corresponding \emph{Rockland} operator…

We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial abnormal minimizers) support interpolation inequalities for optimal transport. A key role is played by sub-Riemannian Jacobi fields and distortion coefficients,…

We prove that for every semigroup of Schwarz maps on the von~Neumann algebra of all bounded linear operators on a Hilbert space which has a subinvariant faithful normal state there exists an associated semigroup of contractions on the space…

In this paper, we study the nonlinear Sobolev type equations on the Heisenberg group. We show that the problems do not admit nontrivial local weak solutions, i.e. "instantaneous blow up" occurs, using the nonlinear capacity method. Namely,…

We consider the H\"older regularity of solutions to the steady Boltzmann equation with in-flow boundary condition in bounded and strictly convex domains $\Omega\subset\mathbb{R}^{3}$ for gases with cutoff soft potential $(-3<\gamma<0)$. We…

In this paper, we consider a semiclassical version of the fractional Klein-Gordon equation on the lattice, $h{\mathbb{Z}}^n.$ Contrary to the Euclidean case that was considered in [2], the discrete fractional Klein-Gordon equation is…