In this paper, we consider the isoperimetric problem in the space R with a density. Our result states that, if the density f is lower semi-continuous and converges to a limit a> 0 at infinity, with f<= a far from the origin, then isoperimetric sets exist for all volumes. Several known results or counterexamples show that the present result is essentially sharp. The special case of our result for radial and increasing densities positively answers a conjecture of Morgan and Pratelli (Ann Glob Anal Geom 43(4):331-365, 2013.
Existence of Isoperimetric Sets with Densities "Converging from Below" on RN
Franzina G;
2017
Abstract
In this paper, we consider the isoperimetric problem in the space R with a density. Our result states that, if the density f is lower semi-continuous and converges to a limit a> 0 at infinity, with f<= a far from the origin, then isoperimetric sets exist for all volumes. Several known results or counterexamples show that the present result is essentially sharp. The special case of our result for radial and increasing densities positively answers a conjecture of Morgan and Pratelli (Ann Glob Anal Geom 43(4):331-365, 2013.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
DepFraPra_17.pdf
accesso aperto
Tipologia:
Versione Editoriale (PDF)
Licenza:
Altro tipo di licenza
Dimensione
518.69 kB
Formato
Adobe PDF
|
518.69 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
