MEAN-VALUE INEQUALITIES IN HILBERT-SPACE

被引：65

作者：

CLARKE, FH ^{[1
]}

LEDYAEV, YS ^{[1
]}

机构：

[1] VA STEKLOV MATH INST,MOSCOW 117966,RUSSIA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 344卷 / 01期

关键词：

MEAN VALUE THEOREM; NONSMOOTH ANALYSIS; FLOW INVARIANCE; MONOTONE FUNCTIONS; GENERALIZED SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS;

D O I：

10.2307/2154718

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish a new mean value theorem applicable to lower semicontinuous functions on Hilbert space. A novel feature of the result is its ''multidirectionality'': it compares the value of a function at a point to its values on a set. We then discuss some refinements and consequences of the theorem, including applications to calculus, flow invariance, and generalized solutions to partial differential equations.

引用

页码：307 / 324

页数：18

共 11 条

[1] A SMOOTH VARIATIONAL PRINCIPLE WITH APPLICATIONS TO SUBDIFFERENTIABILITY AND TO DIFFERENTIABILITY OF CONVEX-FUNCTIONS [J].