A note on non lower semicontinuous perimeter functionals on partitions

Annibale  Magni; Matteo Novaga; Annibale  Magni; Matteo Novaga

doi:10.3934/nhm.2016006

Networks and Heterogeneous Media

2016, Volume 11, Issue 3: 501-508. doi: 10.3934/nhm.2016006

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A note on non lower semicontinuous perimeter functionals on partitions

Annibale Magni ^{1
,},
Matteo Novaga ^{2
,}

1.
Westfälische-Wilhelms Universität Münster, Einsteinstrasse 62, 48149 Münster
2.
Dipartimento di Matematica, Universitá di Pisa, Largo Bruno Pontecorvo 5, I-56127 Pisa

Received: 01 May 2015 Revised: 01 August 2015
Primary: 49Q20; Secondary: 76M30, 76T30.

We consider isotropic non lower semicontinuous weighted perimeter functionals defined on partitions of domains in $\mathbb{R}^n$. Besides identifying a condition on the structure of the domain which ensures the existence of minimizing configurations, we describe the structure of such minima, as well as their regularity.
- Semicontinuity,
- minimal partitions,
- regularity of interfaces
Citation: Annibale Magni, Matteo Novaga. A note on non lower semicontinuous perimeter functionals on partitions[J]. Networks and Heterogeneous Media, 2016, 11(3): 501-508. doi: 10.3934/nhm.2016006

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Abstract

We consider isotropic non lower semicontinuous weighted perimeter functionals defined on partitions of domains in $\mathbb{R}^n$. Besides identifying a condition on the structure of the domain which ensures the existence of minimizing configurations, we describe the structure of such minima, as well as their regularity.

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