Calculus of Variations and Geometric Measure Theory
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M. Novaga - F. Onoue

Existence of minimizers for a generalized liquid drop model with fractional perimeter

created by onoue on 29 Dec 2021
modified by novaga on 01 Jan 2022

[BibTeX]

Preprint

Inserted: 29 dec 2021
Last Updated: 1 jan 2022

Pages: 37
Year: 2021

ArXiv: 2112.14505 PDF

Abstract:

We consider the minimization problem of the functional given by the sum of the fractional perimeter and a general Riesz potential, which is one generalization of Gamow's liquid drop model. We first show the existence of minimizers for any volumes if the kernel of the Riesz potential decays faster than that of the fractional perimeter. Secondly, we show the existence of generalized minimizers for any volumes if the kernel of the Riesz potential just vanishes at infinity. Finally, we study the asymptotic behavior of minimizers when the volume goes to infinity and we prove that a sequence of minimizers converges to the Euclidean ball up to translations if the kernel of the Riesz potential decays sufficiently fast.

Keywords: Nonlocal perimeter, Liquid drop model, generalized minimizers


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