等周锥与部分过定问题的极小解

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2019-05-24 DOI:10.5565/publmat6512102

F. Pacella, G. Tralli

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引用次数: 8

摘要

在本文中，我们考虑了[18]中锥内域中的部分超定混合边值问题。我们证明了在具有等周性的圆锥中，唯一允许解并且最小化扭转能量泛函的域是以圆锥顶点为中心的球面扇区。我们还证明了在$C^{1,1}$度量中与等周度量接近的锥也是等周度量，推广了[1]的结果。这是通过使用圆锥中恒定平均曲率极图的特征来实现的，这改进了[18]的结果。

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Isoperimetric cones and minimal solutions of partial overdetermined problems

In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a torsional energy functional are spherical sectors centered at the vertex of the cone. We also show that cones close in the $C^{1,1}$-metric to an isoperimetric one are also isoperimetric, generalizing so a result of [1]. This is achieved by using a characterization of constant mean curvature polar graphs in cones which improves a result of [18].

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来源期刊

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.