Results 61 to 70 of about 553 (167)

One-side Liouville theorems under an exponential growth condition for Kolmogorov operators

Analysis and Geometry in Metric Spaces
It is known that for a possibly degenerate hypoelliptic Ornstein-Uhlenbeck (OU) operator L=12tr(QD2)+⟨Ax,D⟩=12div(QD)+⟨Ax,D⟩,x∈RN,L=\frac{1}{2}\hspace{0.1em}\text{tr}\hspace{0.1em}\left(Q{D}^{2})+\langle Ax,D\rangle =\frac{1}{2}\hspace{0.1em}\text{div ...
Priola Enrico
doaj   +1 more source

The Metivier inequality and ultradifferentiable hypoellipticity

Mathematische Nachrichten, Volume 297, Issue 7, Page 2517-2531, July 2024.
Abstract In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of L2$L^2$‐solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when
Paulo D. Cordaro, Stefan Fürdös
wiley   +1 more source

Quantitative rates of convergence to equilibrium for the degenerate linear Boltzmann equation on the torus

Bulletin of the London Mathematical Society, Volume 56, Issue 3, Page 981-1003, March 2024.
Abstract We study the linear relaxation Boltzmann equation on the torus with a spatially varying jump rate which can be zero on large sections of the domain. In Bernard and Salvarani (Arch. Ration. Mech. Anal. 208 (2013), no. 3, 977–984), Bernard and Salvarani showed that this equation converges exponentially fast to equilibrium if and only if the jump
Josephine Evans, Iván Moyano
wiley   +1 more source

The Cheeger problem in abstract measure spaces

Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.
Abstract We consider nonnegative σ$\sigma$‐finite measure spaces coupled with a proper functional P$P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant and on Cheeger sets to this setting, requiring minimal assumptions on the pair measure space perimeter ...
Valentina Franceschi, Andrea Pinamonti, Giorgio Saracco, Giorgio Stefani   +3 more
wiley   +1 more source

Blow-up of solutions of nonlinear heat equation with hypoelliptic operators on graded Lie groups [PDF]

, 2019
In this paper we show blow-up of solutions of the nonlinear heat equation with the Rockland operators on the graded Lie groups. In addition, we give the necessary conditions for the existence of local or global solutions of the nonlinear heat equation ...
Tokmagambetov, Niyaz, Bekbolat, Bayan, Kassymov, Aidyn   +2 more
core   +1 more source

Perturbations of Globally Hypoelliptic Operators

Journal of Differential Equations, 1994
The author investigates when perturbations of globally hypoelliptic (GH) operators on a torus are again GH. It is shown that nonelliptic, constant coefficient, first order operators become generically non-GH whereas operators of order bigger or equal to three possess a stability.
openaire   +1 more source

Hypoellipticity for a class of operators with multiple characteristics [PDF]

Journal d'Analyse Mathématique, 2007
The authors consider a class of pseudo-differential operators, with symplectic characteristics of multiplicity 4, having as example in \(\mathbb{R}^2\) \[ P= (D^2_{x_1}+ x^{2h}_1 D^2_{x_2})^2+\lambda x^{h-3}_1 D_{x_2}, \] with \(H\geq 3\). In general, two smooth conic manifolds \(\Sigma_1\) and \(\Sigma_2\) in \(T^*\mathbb{R}^n\) are fixed with ...
MUGHETTI, MARCO, F. Nicola
openaire   +2 more sources

On a class of hypoelliptic evolution operators [PDF]

, 1994
We show that Hypoelliptic Kolmogorov equations are invariant with respect to a suitable Lie group structure. We prove a Harnack inequality which is invariant with respet to the Lie group structure.
E. Lanconelli, POLIDORO, Sergio
core  

A parametrix for stable step two hypoelliptic partial differential operators [PDF]

, 1997
grantor: University of TorontoThe purpose of this thesis is to calculate a parametrix for step two hypoelliptic partial differential operators which are defined on a manifold and satisfy a stability hypothesis. The calculations are based on the
Doolittle, Edward Jon
core   +3 more sources

Harnack inequalities for hypoelliptic evolution operators: geometric issues and applications

Bruno Pini Mathematical Analysis Seminar, 2012
We consider linear second order Partial Differential Equations in the form of "sum of squares of Hörmander vector fields plus a drift term" on a given domain.
Sergio Polidoro
doaj