Open AccessOn the regularity of weak solutions to H-systems
Author(s) -
Roberta Musina
Publication year - 2007
Publication title -
atti della accademia nazionale dei lincei. rendiconti lincei. matematica e applicazioni
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.824
H-Index - 28
eISSN - 1720-0768
pISSN - 1120-6330
DOI - 10.4171/rlm/490
Subject(s) - mathematics
We prove that every weak solution to the H-surface equation is locally bounded, provided the prescribed mean curvature H satisfies a suitable condition at infinity. No smoothness assumption is required on H. We also consider the Dirichlet problem for the H-surface equation on a bounded regular domain with boundedboundary data and the H-bubble problem. Under the same assumptions on H, we prove that every weak solution is globally bounded