Axisymmetric mixed free boundary value problem

Abstract

Mixed Free Boundary Value Problem for Laplace equation in axisymmetrical case is considered. We take into consideration mean and Gauss curvatures of the free boundary. The problem of this type arise on investigating thermal equillibrium of two phases. We take into account capillary forces acting in intermediate layer separating different phases. Plane model of the equillibrium without capillary forces was considered in the paper([1]). We consider variational problem whose solution is generalized solution of the boundary value problem.We prove regularity of solution, analyticity of free boundary and investigate its properties.