We prove a sufficient criterion to determine if a planar set Ω minimizes the prescribed curvature functional F_κ[E]:= P(E)−κ|E| amongst E ⊂ Ω. As a special case, we derive a sufficient criterion to determine if Ω is a self-Cheeger set, i.e. if it minimizes the ratio P(E)/|E| among all of its subsets. As a side effect we provide a way to build self-Cheeger sets.
A sufficient criterion to determine planar self-Cheeger sets / Saracco G.. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - ELETTRONICO. - 28:(2021), pp. 951-958.
A sufficient criterion to determine planar self-Cheeger sets
Saracco G.
2021
Abstract
We prove a sufficient criterion to determine if a planar set Ω minimizes the prescribed curvature functional F_κ[E]:= P(E)−κ|E| amongst E ⊂ Ω. As a special case, we derive a sufficient criterion to determine if Ω is a self-Cheeger set, i.e. if it minimizes the ratio P(E)/|E| among all of its subsets. As a side effect we provide a way to build self-Cheeger sets.
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