Symmetry-breaking bifurcation of analytic solutions to free boundary problems: An application to a model of tumor growth

In this paper we develop a general technique for establishing analyticity o f solutions of partial differential equations which depend on a parameter e psilon. The technique is worked out primarily for a free boundary problem d escribing a model of a stationary tumor. We prove the existence of infinite ly many branches of symmetry-breaking solutions which bifurcate from any gi ven radially symmetric steady state; these asymmetric solutions are analyti c jointly in the spatial variables and in epsilon.