We carry out an analysis of the size of the contact surface between a Cheeger set E and its ambient space Ω⊂Rd. By providing bounds on the Hausdorff dimension of the contact surface ∂E∩∂Ω, we show a fruitful interplay between this size itself and the regularity of the boundaries. Eventually, we obtain sufficient conditions to infer that the contact surface has positive (d−1) dimensional Hausdorff measure. Finally we prove by explicit examples in two dimensions that such bounds are optimal.
Dimensional lower bounds for contact surfaces of Cheeger sets
Caroccia M.;
2021-01-01
Abstract
We carry out an analysis of the size of the contact surface between a Cheeger set E and its ambient space Ω⊂Rd. By providing bounds on the Hausdorff dimension of the contact surface ∂E∩∂Ω, we show a fruitful interplay between this size itself and the regularity of the boundaries. Eventually, we obtain sufficient conditions to infer that the contact surface has positive (d−1) dimensional Hausdorff measure. Finally we prove by explicit examples in two dimensions that such bounds are optimal.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Dimensional_lower_bounds_for_contact_surfaces_of_Cheeger_sets.pdf
Accesso riservato
:
Publisher’s version
Dimensione
1.12 MB
Formato
Adobe PDF
|
1.12 MB | Adobe PDF | Visualizza/Apri |
|
11311-1196717_Caroccia.pdf
Open Access dal 02/01/2024
:
Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione
1.15 MB
Formato
Adobe PDF
|
1.15 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
