Necessary conditions and non-existence results for autonomous nonconvex variational problems

被引：11

作者：

Cupini, Giovanni ^{[1
]}

Guidorzi, Marcello ^{[2
]}

Marcelli, Cristina ^{[2
]}

机构：

[1] Univ Florence, Dipartimento Matemat U Dini, I-50134 Florence, Italy

[2] Univ Politecn Marche, Dipartimento Sci Matemat, I-60131 Ancona, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 243卷 / 02期

关键词：

autonomous variational problem; necessary condition; DuBois-Reymond condition; non-existence result; subdifferential; maximum principle;

D O I：

10.1016/j.jde.2007.05.035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：329 / 348

页数：20

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