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

被引：1

作者：

Cerny, Robert ^{[1
]}

Hencl, Stanislav ^{[1
]}

Kolar, Jan ^{[2
]}

机构：

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

[2] Acad Sci Czech Republic, Inst Math, CR-11567 Prague 1, Czech Republic

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 7-8期

关键词：

Weak continuity; Nonlinear integral functional; Sobolev spaces; Linearity;

D O I：

10.1016/j.na.2009.01.117

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Omega subset of N-R be a bounded open set and let g: Omega x R -> R be a Caratheodory function that satisfies standard growth conditions. Then the functional Phi(u) = integral(Omega) g (x, u(x)) dx is weakly continuous on W-0(1,p)(Omega), 1 <= p <= infinity, if and only if g is linear in the second variable. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：2753 / 2763

页数：11

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