Bernoulli free-boundary problems in strip-like domains and a property of permanent waves in water of finite depth
arXiv:0708.4371
Abstract
We study weak solutions for a class of free boundary problems which includes as a special case the classical problem of traveling 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.