变分微积分和Aronsson-Euler方程解的一个性质

IF 1.5 3区数学 Q1 MATHEMATICS Advances in Differential Equations Pub Date : 2021-06-30 DOI:10.57262/ade028-0304-287

Camilla Brizzi, L. Pascale

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引用次数: 3

摘要

我们发现了极限泛函的绝对极小值的一个新的极小性，它的变分问题也称为L∞变分问题。特别是对于拟凸泛函的每一个极小值v。因此，我们认为该集合有适当的定义。如果u是一个绝对最小化器，我们给出a (u)的结构结果，并证明对于每个最小化器v, a (u)∧a (v)。摘要我们发现了极限泛函的绝对极小值的一个新的极小性(也称为L∞变分问题)。

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A property of Absolute Minimizers in $L^\infty$ Calculus of Variations and of solutions of the Aronsson-Euler equation

We discover a new minimality property of the absolute minimizers of supremal functionals, whose variational problems are also known as L ∞ variational problems. In particular for every minimizer v of the quasi-convex functional ess . sup we consider the set suitably deﬁned. If u is an absolute minimizer we give a structure result for A ( u ) and we show that then A ( u ) ⊂ A ( v ) for every minimizer v . Abstract. We discover a new minimality property of the absolute minimizers of supremal functionals (also known as L ∞ Calculus of Variations problems).

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来源期刊

Advances in Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.