吉尔伯特-斯坦纳问题的一个凸方法

IF 1.2 4区数学 Q1 MATHEMATICS

Interfaces and Free Boundaries Pub Date : 2018-10-12 DOI:10.4171/ifb/436

M. Bonafini, 'Edouard Oudet

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引用次数: 5

摘要

我们在R^d$和流形上描述了Gilbert-Steiner问题的凸松弛，扩展了[9]中提出的框架，并通过校准型参数讨论了其锐度。最小化所产生的问题，然后处理数值，我们提出的结果为一组广泛的例子。特别是我们能够解决曲面上的斯坦纳树问题。

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A convex approach to the Gilbert–Steiner problem

We describe a convex relaxation for the Gilbert-Steiner problem both in $R^d$ and on manifolds, extending the framework proposed in [9], and we discuss its sharpness by means of calibration type arguments. The minimization of the resulting problem is then tackled numerically and we present results for an extensive set of examples. In particular we are able to address the Steiner tree problem on surfaces.

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来源期刊

Interfaces and Free Boundaries 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Interfaces and Free Boundaries is dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems in all areas where such phenomena are pertinent. The journal aims to be a forum where mathematical analysis, partial differential equations, modelling, scientific computing and the various applications which involve mathematical modelling meet. Submissions should, ideally, emphasize the combination of theory and application.