The existence of solutions to variational problems of slow growth

被引：1

作者：

Cellina, Arrigo ^{[1
]}

Staicu, Vasile ^{[2
,3
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via R Cozzi 53, I-20125 Milan, Italy

[2] Univ Aveiro, CIDMA, Campus Univ Santiago, P-3810193 Aveiro, Portugal

[3] Univ Aveiro, Dept Math, Campus Univ Santiago, P-3810193 Aveiro, Portugal

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 07期

关键词：

CLASSICAL PROBLEM; FUNCTIONALS; CALCULUS;

D O I：

10.1016/j.jde.2015.12.025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the existence of solutions, in the space W-1,W-1(Omega), to the problem minimize integral(Omega) L(del v(x))dx on phi + W-0(1,1) (Omega) where L is of slow (linear or at most quadratic) growth. We present a necessary and sufficient condition in order that, for any smooth boundary datum phi and for any bounded Omega with smooth boundary, the minimum problem be solvable. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：5834 / 5846

页数：13

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