Maximum principles for infinite dimensional diffusion equations
type: Item
instance of: scholarly article
title: Maximum principles for infinite dimensional diffusion equations
zbMATH Open document ID: 1119.35109
author: Roberto Stasi
published in: Potential Analysis
publication date: 2007-04-10T00:00:00Z
review text: The author is concerned with the following differential operator: \[ \mathcal{L}\varphi(x)=\tfrac{1}{2} \operatorname{Tr}[Q(x)D^2\varphi(x)]+\langle Ax+g(x), D\varphi(x)\rangle,\quad x\in D(A). \] Here \(Q(x)\) is a symmetric positive linear operator on a Hilbert space \(H\), \(A:D(A)\subset H\to H\) a linear operator and \(g:H\to H\) a nonlinear mapping. Elliptic equations \[ \lambda\varphi(x)-\mathcal{L}\varphi(x)=f(x),\quad x\in D(A) \] and parabolic equations \[ \begin{aligned} \frac{\partial u}{\partial t}(t, x)&=\mathcal{L}u(t, x), \quad t\geq 0,\;x\in D(A),\\ u(0, x)&=u_0(x), \quad x\in H \end{aligned} \] are studied. Validity of the maximum principle is proved.
reviewed by: Nikita Ratanov
Mathematics Subject Classification ID: 35R15
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 46G12
Mathematics Subject Classification ID: 58C20
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 5141544
zbMATH Keywords: maximum principle
zbMATH Keywords: Kolmogorov equations
MaRDI profile type: Publication
full work available at URL: s11118-005-9000-2
OpenAlex ID: W1985002617
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DOI: 10.1007/S11118-005-9000-2
description: scientific article; zbMATH DE number 5141544