THE HIGHER INTEGRABILITY AND THE VALIDITY OF THE EULER-LAGRANGE EQUATION FOR SOLUTIONS TO VARIATIONAL PROBLEMS

被引：8

作者：

Bonfanti, Giovanni ^{[1
]}

Cellina, Arrigo ^{[1
]}

Mazzola, Marco ^{[1
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicazioni, I-20125 Milan, Italy

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2012年 / 50卷 / 02期

关键词：

calculus of variations; necessary conditions; Euler-Lagrange equation;

D O I：

10.1137/110820890

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We prove higher integrability properties of solutions to the problem of minimizing integral(Omega) L(x, u(x), del u(x)) dx, where xi bar right arrow L(x, u, xi) is a convex function satisfying some additional conditions. As an application, we prove the validity of the Euler-Lagrange equation for a class of functionals with growth faster than exponential.

引用

页码：888 / 899

页数：12

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