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 BVloc(Omega). We also provide an example which shows that such regularity result is optimal.
Regularity results for some 1-homogeneous functionals / NOVAGA MATTEO; E. PAOLINI. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - STAMPA. - 3:(2002), pp. 555-566. [10.1016/S1468-1218(01)00048-7]
Regularity results for some 1-homogeneous functionals
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 BVloc(Omega). We also provide an example which shows that such regularity result is optimal.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.