We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general theory to characterize the limits of s-fractional mean curvature flows as (Formula presented.) and (Formula presented.) In analogy with the s-fractional mean curvature flows, we introduce the notion of s-Riesz curvature flows and characterize its limit as (Formula presented.) Eventually, we discuss the limit behavior as (Formula presented.) of the flow generated by a regularization of the r-Minkowski content.

Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows / Cesaroni, A.; De Luca, L.; Novaga, M.; Ponsiglione, M.. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 46:7(2021), pp. 1344-1371. [10.1080/03605302.2021.1875485]

Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows

Cesaroni A.;Novaga M.;Ponsiglione M.
2021

Abstract

We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general theory to characterize the limits of s-fractional mean curvature flows as (Formula presented.) and (Formula presented.) In analogy with the s-fractional mean curvature flows, we introduce the notion of s-Riesz curvature flows and characterize its limit as (Formula presented.) Eventually, we discuss the limit behavior as (Formula presented.) of the flow generated by a regularization of the r-Minkowski content.
2021
35D40; 35K93; 35R11; 53C44; fractional mean curvature flow; fractional perimeter; level set formulation; local and nonlocal geometric evolutions; Minkowski content; riesz energy; viscosity solutions
01 Pubblicazione su rivista::01a Articolo in rivista
Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows / Cesaroni, A.; De Luca, L.; Novaga, M.; Ponsiglione, M.. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 46:7(2021), pp. 1344-1371. [10.1080/03605302.2021.1875485]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1612350
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