Sharp estimates of the distance from a fixed point to the frontier of a Hele-Shaw flow
The paper deals with the global shape of a Hele-Shaw flow, produced by the injection of fluid into the narrow gap between two parallel planes. The author translates the problem into a problem concerning the shape of a quadrature domain of a finite positive measure for subharmonic functions. After establishing the existence of quadrature domains, one gives sharp estimates of the distance from a fixed point to the frontier of the domain.
finite positive measure for subharmonic functions
scientific article; zbMATH DE number 1199890