The Hele-Shaw problem with surface tension in a half-plane: A model problem

Consider the Hele-Shaw problem with surface tension in the half-plane {y(1) > 0) when at time t = 0 the domain Omega(t) lies partly on the line y(1) = 0, and partly in {y(1) > 0}. In order to establish existence of a solution to this free boundary problem we need to study the (linear) model problem when the Q(t) is a fixed angular domain. In this paper we consider this model problem and establish existence of a solution satisfying sharp weighted Holder estimates. These estimates will be used in subsequent work to solve the full Hele-Shaw problem. (c) 2005 Elsevier Inc. All rights reserved.