a1 Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.
(Received May 08 2007)
(Accepted November 08 2007)