Integral functionals that are continuous with respect to the weak topology on W01,p (0,1)

被引：2

作者：

Hencl, S

Kolár, J

Pangrác, O

机构：

[1] Charles Univ Prague, Dept Math Anal, Prague 18600 8, Czech Republic

[2] Charles Univ Prague, Dept Appl Math, CR-11800 Prague, Czech Republic

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 63卷 / 01期

关键词：

weak continuity; nonlinear integral functional; Sobolev spaces; linearity;

D O I：

10.1016/j.na.2005.05.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For continuous (or, locally bounded Caratheodory) functions g: [0, 1] x R -> R we prove that the functional Phi(u) = integral(1)(0)g (x, u (x)) dx is weakly continuous on W-0(1,p)(0, 1), 1 <= p < infinity, if and only if g is linear in the second variable. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：81 / 87

页数：7