We consider local minimizers for a class of 1-homogeneous integral functionals defined on BVloc(Omega), with Omega subset of R-2. Under general assumptions on the functional, we prove that the boundary of the subgraph of such minimizers is (locally) a lipschitz graph in a suitable direction. The proof of this statement relies on a regularity result holding for boundaries in R-2 which minimize an anisotropic perimeter. This result is applied to the boundary of sublevel sets of a minimizer u is an element of BV_loc(Omega).

Regularity results for some 1-homogeneous functionals

NOVAGA, MATTEO;PAOLINI, EMANUELE
2002

Abstract

We consider local minimizers for a class of 1-homogeneous integral functionals defined on BVloc(Omega), with Omega subset of R-2. Under general assumptions on the functional, we prove that the boundary of the subgraph of such minimizers is (locally) a lipschitz graph in a suitable direction. The proof of this statement relies on a regularity result holding for boundaries in R-2 which minimize an anisotropic perimeter. This result is applied to the boundary of sublevel sets of a minimizer u is an element of BV_loc(Omega).
Novaga, Matteo; Paolini, Emanuele
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/72031
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 4
social impact