Results 51 to 60 of about 553 (167)

A comparison principle for nonlinear heat Rockland operators on graded groups

Bulletin of the London Mathematical Society, Volume 50, Issue 5, Page 753-758, October 2018., 2018
Abstract In this note we show a comparison principle for nonlinear heat Rockland operators on graded groups. We give a simple proof for it using purely algebraic relations. As an application of the established comparison principle we prove the global in t‐boundedness of solutions for a class of nonlinear equations for the heat p‐sub‐Laplacian on ...
Michael Ruzhansky, Durvudkhan Suragan
wiley   +1 more source

Null-controllability of hypoelliptic quadratic differential equations [PDF]

, 2018
46 pagesInternational audienceWe study the null-controllability of parabolic equations associated to a general class of hypoelliptic quadratic differential operators.
Karel Pravda-Starov, Pravda-Starov, Karel, Beauchard, Karine, Karine Beauchard   +3 more
core   +1 more source

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

LOWER ORDER PERTURBATION AND GLOBAL ANALYTIC VECTORS FOR A CLASS OF GLOBALLY ANALYTIC HYPOELLIPTIC OPERATORS [PDF]

, 2016
In this work we return to the class of globally analytic hypoelliptic Hormander's operators defined on the N-dimensional torus introduced by Cordaro and Himonas and prove that if P is any operator in this class, then a perturbation of P by an analytic ...
Jahnke, MR, Chinni, G, Rodrigues, NB, Cordaro, PD   +3 more
core   +1 more source

On a rigidity result for Kolmogorov-type operators

Bruno Pini Mathematical Analysis Seminar
Let D be a bounded open subset of ℝN and let z0 be a point of D. Assume that the Newtonian potential of D is proportional outside D to the potential of a mass concentrated at z0. Then D is a Euclidean ball centred at z0. This theorem, proved by Aharonov,
Alessia E. Kogoj
doaj   +1 more source

The Uncertainty Principle and Hypoelliptic Operators

Publications of the Research Institute for Mathematical Sciences, 1987
Let P be a differential operator of second order with coefficients in \(C^{\infty}(R^ n)\), that is, \[ (1)\quad P=\sum_{j,k}a_{jk}(x)D_ jD_ k+\sum_{j}ib_ j(x)D_ j+c(x),\quad D_ j=-i\partial_{x_ j}. \] We assume that \[ (2)\quad a_{jk}\quad and\quad b_ j\quad are\quad real\quad valued,\quad \sum a_{jk}(x)\xi_ j\xi_ k\geq 0\quad for\quad any\quad (x,\xi)
openaire   +3 more sources

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 a long standing conjecture: positive Liouville Theorem for hypoelliptic Ornstein-Uhlenbeck operators

Bruno Pini Mathematical Analysis Seminar
Let $\mathcal{L}$ be the hypoelliptic Ornstein-Uhlenbeck operator associated with the pair of matrices (A,B). In 2004, Priola and Zabczyk proved the following Liouville-type theorem: every bounded entire solution of $\mathcal{L}u=0$ is constant if and ...
Alessia E. Kogoj, Ermanno Lanconelli, Giulio Tralli   +2 more
doaj   +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

The analysis of the hypoelliptic Laplacian [PDF]

, 2011
This chapter constructs a functional analytic machinery that is adapted to the analysis of the hypoelliptic Laplacian ℒA,bX. The analysis of the hypoelliptic Laplacian essentially consists in the construction of Sobolev spaces on which the operators ℒA ...
Jean-Michel Bismut
core   +1 more source