Limiting subdifferentials of indefinite integrals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:341

Article

Nguyen Huy Chieu

关键词: indefinite integral;    Frechet subdifferential;    limiting subdifferential;    Aumann integral;   

DOI  :  10.1016/j.jmaa.2007.10.020

来源: Elsevier

【 摘 要 】

We compute the limiting subdifferential partial derivative F((x) over bar) of the indefinite integral of the form F(x) = integral(x)(a) f(t)dt where f is an essentially bounded measurable function, or a function continuous on an interval containing (x) over bar is an element of R (except for, possibly, (x) over bar), or a step-function which has a countable number of steps around (x) over bar. The related problem of computing the Aumann integral of the limiting subdifferential mapping partial derivative f(center dot), where f is a Lipschitz real function detined on an open set U subset of C R-n, is also investigated. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free