A new \(L^p\)-Antieigenvalue Condition for Ornstein-Uhlenbeck Operators

In this paper we study perturbed Ornstein-Uhlenbeck operators \begin{align*} \left[ \mathcal{L}_{\infty} v\right](x) = A\triangle v(x) + \left\langle Sx,\nabla v(x)\right\rangle-B v(x),\,x\in\mathbb{R}^d,\,d\geqslant 2, \end{align*} for simultaneously diagonalizable matrices \(A,B\in\mathbb{C}^{N,N}...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2015-10
Main Author: Otten, Denny
Format: Article
Language:English
Subjects:
Alignment
Differential equations
Lagrange multiplier
Mathematical analysis
Matrix methods
Operators (mathematics)
Time dependence
Triangles
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we study perturbed Ornstein-Uhlenbeck operators \begin{align*} \left[ \mathcal{L}_{\infty} v\right](x) = A\triangle v(x) + \left\langle Sx,\nabla v(x)\right\rangle-B v(x),\,x\in\mathbb{R}^d,\,d\geqslant 2, \end{align*} for simultaneously diagonalizable matrices \(A,B\in\mathbb{C}^{N,N}\). The unbounded drift term is defined by a skew-symmetric matrix \(S\in\mathbb{R}^{d,d}\). Differential operators of this form appear when investigating rotating waves in time-dependent reaction diffusion systems. As shown in a companion paper, one key assumption to prove resolvent estimates of \(\mathcal{L}_{\infty}\) in \(L^p(\mathbb{R}^d,\mathbb{C}^N)\), \(1 \frac{|p-2|}{p}, \,1
ISSN:2331-8422