Results 61 to 70 of about 3,513,590 (164)

Hypoellipticity for a class of kinetic equations

Kyoto Journal of Mathematics, 2007
The authors consider the following linearized version of Boltzmann equation without angular cutoff: \[ Pu= \partial_t+ x\nabla_y u+ \sigma(-\widetilde\Delta_x)^\lambda u= f, \] where \((x,y)\in \mathbb{R}^{2n}\) and \(\sigma> 0\). Here \((-\widetilde\Delta_x)^\lambda\) is a Fourier multiplier with symbol \(|\eta|^{2\lambda}\) if \(|\eta|\geq 2\), and \(
Xu, Chao-Jiang, Morimoto, Yoshinori
openaire   +4 more sources

Bounds on Riesz Means of the Eigenvalues for Baouendi–Grushin Type Operators

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
The aim of this paper is to consider spectral inequalities of a class of Baouendi–Grushin type operators in cylinders. Such operators are hypoelliptic and we obtain non‐Weyl type inequalities depending on the rate of the degeneracy. We also give an example where all eigenvalues and eigenfunctions are computed explicitly.
Alaa Aljahili, Ari Laptev, Shikha Binwal
wiley   +1 more source

Disuguaglianze di Harnack alla frontiera per equazioni di Kolmogorov

Bruno Pini Mathematical Analysis Seminar, 2011
We describe some recent results on the boundary regularity for hypoelliptic Kolmogorov equations. We prove boundary Harnack inequalities of the positive solutions to Kolmogorov equations vanishing on some relatively open subset of the boundary ...
Sergio Polidoro
doaj  

Short-time asymptotics of the regularizing effect for semigroups generated by quadratic operators

, 2016
We study accretive quadratic operators with zero singular spaces. These degenerate non-selfadjoint differential operators are known to be hypoelliptic and to generate contraction semigroups which are smoothing in the Schwartz space for any positive time.
Hitrik, Michael, Pravda-Starov, Karel, Viola, Joe   +2 more
core   +2 more sources

Hypoelliptic entropy dissipation for stochastic differential equations

, 2021
Typos corrected.
Feng, Qi, Li, Wuchen
openaire   +2 more sources

Dunkl convolution and elliptic regularity for Dunkl operators

Mathematische Nachrichten, Volume 297, Issue 12, Page 4416-4436, December 2024.
Abstract We discuss in which cases the Dunkl convolution u∗kv$u*_kv$ of distributions u,v$u,v$, possibly both with non‐compact support, can be defined and study its analytic properties. We prove results on the (singular‐)support of Dunkl convolutions.
Dominik Brennecken
wiley   +1 more source

A symplectic extension map and a new Shubin class of pseudo-differential operators

, 2014
For an arbitrary pseudo-differential operator $A:\mathcal{S}(\mathbb{R}% ^{n})\longrightarrow\mathcal{S}^{\prime}(\mathbb{R}^{n})$ with Weyl symbol $a\in\mathcal{S}^{\prime}(\mathbb{R}^{2n})$, we consider the pseudo-differential operators $\widetilde{A}:\
Bastos, Bastos, Bayen, Bayen, Bondar, Bondar, Bopp, de Gosson, de Gosson, de Gosson, de Gosson, de Gosson, de Gosson, Dias, Dias, Dias, Dias, Dias, Folland, João Nuno Prata, Landau, Leray, Maurice A. de Gosson, Nuno Costa Dias, Shubin, Wong   +25 more
core   +1 more source

The quantization of Maxwell theory in the Cauchy radiation gauge: Hodge decomposition and Hadamard states

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract The aim of this paper is to prove the existence of Hadamard states for the Maxwell equations on any globally hyperbolic spacetime. This will be achieved by introducing a new gauge fixing condition, the Cauchy radiation gauge, that will allow to suppress all the unphysical degrees of freedom. The key ingredient for achieving this gauge is a new
Simone Murro, Gabriel Schmid
wiley   +1 more source

On curvature bounds in Lorentzian length spaces

Journal of the London Mathematical Society, Volume 110, Issue 2, August 2024.
Abstract We introduce several new notions of (sectional) curvature bounds for Lorentzian pre‐length spaces: On the one hand, we provide convexity/concavity conditions for the (modified) time separation function, and, on the other hand, we study four‐point conditions, which are suitable also for the non‐intrinsic setting. Via these concepts, we are able
Tobias Beran, Michael Kunzinger, Felix Rott   +2 more
wiley   +1 more source

Hypoellipticity and Higher Order Levi Conditions

, 2014
We study the $C^\infty$-hypoellipticity for a class of double characteristic operators with simplectic characteristic manifold, in the case the classical condition of minimal loss of derivatives is ...
Mughetti, Marco
core   +1 more source