具有自然Orlicz增长的高阶拟凸积分的极小值的部分正则性。

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2025-01-01 Epub Date: 2025-01-24 DOI:10.1007/s10231-025-01547-2

Christopher Irving

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引用次数: 0

摘要

给出了k阶泛函在拟凸性和一般生长条件下的极小值的部分正则性定理。我们将假设一个由满足Δ 2和∇2条件的n函数控制的自然增长条件，假设对被积函数的二阶导数没有定量估计；即使在k = 1的情况下，这也是新的。这些结果也将推广到强局部极小值的情况。

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Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth.

A partial regularity theorem is presented for minimisers of $k^{th}$ -order functionals subject to a quasiconvexity and general growth condition. We will assume a natural growth condition governed by an N-function satisfying the $Δ_{2}$ and $\nabla_{2}$ conditions, assuming no quantitative estimates on the second derivative of the integrand; this is new even in the $k = 1$ case. These results will also be extended to the case of strong local minimisers.

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.