We consider the volume-preserving geometric evolution of the boundary of a set under fractional mean curvature. We show that smooth convex solutions maintain their fractional curvatures bounded for all times, and the long-time asymptotics approach round spheres. The proofs are based on a priori estimates on the inner and outer radii of the solutions.

Cinti, E., Sinestrari, C., Valdinoci, E. (2020). CONVEX SETS EVOLVING BY VOLUME-PRESERVING FRACTIONAL MEAN CURVATURE FLOWS. ANALYSIS & PDE, 13(7), 2149-2171 [10.2140/apde.2020.13.2149].

CONVEX SETS EVOLVING BY VOLUME-PRESERVING FRACTIONAL MEAN CURVATURE FLOWS

SINESTRARI C.;VALDINOCI E.
2020-01-01

Abstract

We consider the volume-preserving geometric evolution of the boundary of a set under fractional mean curvature. We show that smooth convex solutions maintain their fractional curvatures bounded for all times, and the long-time asymptotics approach round spheres. The proofs are based on a priori estimates on the inner and outer radii of the solutions.
2020
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
geometric evolution equations, fractional partial differential equations, fractional perimeter, fractional mean curvature flow, asymptotic behavior of solutions
Cinti, E., Sinestrari, C., Valdinoci, E. (2020). CONVEX SETS EVOLVING BY VOLUME-PRESERVING FRACTIONAL MEAN CURVATURE FLOWS. ANALYSIS & PDE, 13(7), 2149-2171 [10.2140/apde.2020.13.2149].
Cinti, E; Sinestrari, C; Valdinoci, E
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/261807
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