Preservation of convexity of solutions to parabolic equations

被引：26

作者：

Janson, S ^{[1
]}

Tysk, J ^{[1
]}

机构：

[1] Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2004年 / 206卷 / 01期

关键词：

parabolic equation; convexity;

D O I：

10.1016/j.jde.2004.07.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper we find necessary and sufficient conditions on the coefficients of a parabolic equation for convexity to be preserved. A parabolic equation is said to preserve convexity if given a convex initial condition, any solution of moderate growth remains a convex function of the spatial variables for each fixed time. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：182 / 226

页数：45

共 8 条

[1]

[Anonymous], 1975, Stochastic differential equations and applications

[2] General properties of option prices [J].

Bergman, YZ ;

Grundy, BD ;

Wiener, Z .

JOURNAL OF FINANCE, 1996, 51 (05) :1573-1610

[3]

Eidelman S.D., 1969, PARABOLIC SYSTEMS, P469

[4]

Friedman A., 1964, Partial Differential Equations of Parabolic Type

[5]

Hobson DG, 1998, ANN APPL PROBAB, V8, P193

[6]

Janson S, 2003, ANN APPL PROBAB, V13, P890

[7]

Treves F., 1967, TOPOLOGICAL VECTOR S

[8]

WANG MT, 2002, ARXIVMATHAP0209175

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