The isoperimetric problem for nonlocal perimeters

Annalisa Cesaroni; Matteo Novaga

doi:10.3934/dcdss.2018023

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2018, Volume 11, Issue 3: 425-440. Doi: 10.3934/dcdss.2018023

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The isoperimetric problem for nonlocal perimeters

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: May 2017

Revised: August 2017

Published: June 2018

The authors were supported the Fondazione CaRiPaRo Project "Nonlinear Partial Differential Equations: Asymptotic Problems and Mean-Field Games", Project PRA 2017 of the University of Pisa "Problemi di ottimizzazione e di evoluzione in ambito variazionale", the INdAM-GNAMPA project "Tecniche EDP, dinamiche e probabilistiche per lo studio di problemi asintotici".

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Abstract

We consider a class of nonlocal generalized perimeters which includes fractional perimeters and Riesz type potentials. We prove a general isoperimetric inequality for such functionals, and we discuss some applications. In particular we prove existence of an isoperimetric profile, under suitable assumptions on the interaction kernel.

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

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References

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