Volume constrained minimizers of the fractional perimeter with a potential energy

Annalisa Cesaroni; Matteo Novaga

doi:10.3934/dcdss.2017036

Article Contents

2017, Volume 10, Issue 4: 715-727. Doi: 10.3934/dcdss.2017036

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Volume constrained minimizers of the fractional perimeter with a potential energy

Annalisa Cesaroni^1, and
Matteo Novaga^2, ,

1.
Department of Statistical Sciences, University of Padova, Via Cesare Battisti 141,35121 Padova, Italy
2.
Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5,56127 Pisa, Italy

^* Corresponding author
^* Corresponding author

Received: March 2016

Revised: May 2016

Published: July 2017

The authors were supported by the Italian GNAMPA and by the University of Pisa via grant PRA-2015-0017.

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Abstract

We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume integral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove existence and regularity of minimizers under suitable assumptions on the potential energy, which cover the periodic case. In the small volume regime we show that minimizers are close to balls, with a quantitative estimate.

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Mathematics Subject Classification: 53A10, 49Q20, 35R11.

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References

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