We give an elementary proof for the well known regularity theorem of boundary with prescribed mean curvature for the case of planar subgraphs whose variational curvature belongs to $L^p(\R^2), p>2. The proof is based upon ideas already introduced in the precedent paper. Finally we give an example of a subgraph E of a C^infinity-function with H_E in L^1(\R^2)) but H_E not in L^p(\R^2), for all p>1.
The variational cost of the change of direction in a planar curve and application to regularity of 2-dimensional sets / Barozzi, Elisabetta; Massari, U.. - In: ANNALI DELL'UNIVERSITÀ DI FERRARA. SEZIONE 7: SCIENZE MATEMATICHE. - ISSN 0430-3202. - 61:1(2015), pp. 1-16. [10.1007/s11565-014-0209-0]
The variational cost of the change of direction in a planar curve and application to regularity of 2-dimensional sets
Barozzi, Elisabetta;
2015-01-01
Abstract
We give an elementary proof for the well known regularity theorem of boundary with prescribed mean curvature for the case of planar subgraphs whose variational curvature belongs to $L^p(\R^2), p>2. The proof is based upon ideas already introduced in the precedent paper. Finally we give an example of a subgraph E of a C^infinity-function with H_E in L^1(\R^2)) but H_E not in L^p(\R^2), for all p>1.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
