Preservation of convexity of solutions to parabolic equations
type: Item
instance of: scholarly article
title: Preservation of convexity of solutions to parabolic equations
zbMATH Open document ID: 1056.35011
author: Svante Janson
author: Johan Tysk
published in: Journal of Differential Equations
publication date: 2004-11-18T00:00:00Z
review text: This paper is a continuation of the authors' earlier paper in Ann. Appl. Probab. 13, 890--913 (2003; Zbl 1061.91028), where only the case of one space variables was considered in connection with applications to finance. It deals with the Cauchy problem \[ M F(x,t) = h(x,t), \qquad F(x,0) = f(x), \qquad x \in \mathbb R^n, \;0 \leq t \leq T \] with \[ M = \frac{\partial}{\partial t} - L, \] \(L\) being a linear elliptic operator of second order with coefficients depending on \(x, t\). The aim of the paper is to find conditions on \(M, h\) assuring that for every fixed \(t\) the unique solution \(F(x,t)\) is convex in space variables if \(f(x)\) it does. Several examples of such operators \(M\) are given.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 2116222
zbMATH Keywords: convex in space variables
reviewed by: Hanna Marcinkowska
MaRDI profile type: Publication
full work available at URL: j.jde.2004.07.016
OpenAlex ID: W2011789674
cites work: Q5520962
cites work: Q4086524
cites work: Volatility misspecification, option pricing and superreplication via coupling
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DOI: 10.1016/J.JDE.2004.07.016
description: scientific article; zbMATH DE number 2116222