Connected perimeter of planar sets-Reference-Cited by-同舟云学术

Connected perimeter of planar sets

Published:2020-05-12 Issue:0 Volume:0 Page:
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Dayrens François¹,Masnou Simon¹,Novaga Matteo²,Pozzetta Marco²

Affiliation:

1. Univ Lyon , Université Claude Bernard Lyon 1 , CNRS UMR 5208, Institut Camille Jordan, 43 Bd du 11 novembre 1918, 69622 Villeurbanne Cedex , France

2. Dipartimento di Matematica , Università di Pisa , Largo Bruno Pontecorvo 5, 56127 Pisa , Italy

Abstract

Abstract We introduce a notion of connected perimeter for planar sets defined as the lower semicontinuous envelope of perimeters of approximating sets which are measure-theoretically connected. A companion notion of simply connected perimeter is also studied. We prove a representation formula which links the connected perimeter, the classical perimeter, and the length of suitable Steiner trees. We also discuss the application of this notion to the existence of solutions to a nonlocal minimization problem with connectedness constraint.

Funder

Agence Nationale de la Recherche

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2019-0050/pdf

Reference17 articles.

1. L. Ambrosio, V. Caselles, S. Masnou and J.-M. Morel, Connected components of sets of finite perimeter and applications to image processing, J. Eur. Math. Soc. (JEMS) 3 (2001), no. 1, 39–92.

2. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., Oxford University, New York, 2000.

3. M. Bonnivard, A. Lemenant and V. Millot, On a phase field approximation of the planar Steiner problem: Existence, regularity, and asymptotic of minimizers, Interfaces Free Bound. 20 (2018), no. 1, 69–106.

4. M. Bonnivard, A. Lemenant and F. Santambrogio, Approximation of length minimization problems among compact connected sets, SIAM J. Math. Anal. 47 (2015), no. 2, 1489–1529.

5. P. W. Dondl, A. Lemenant and S. Wojtowytsch, Phase field models for thin elastic structures with topological constraint, Arch. Ration. Mech. Anal. 223 (2017), no. 2, 693–736.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Periodic partitions with minimal perimeter;Nonlinear Analysis;2024-06