Analyticity of solutions to a free boundary problem modeling the growth of multi-layer tumors

In this paper we study the analyticity of solutions to a free boundary problem modeling the growth of multi-layer tumors. The problem consists of three elliptic equations defined on a strip-like domain in Rn+1Rn+1, with one part of the boundary moving and a priori unknown. The evolution of the moving boundary is governed by a Stefan type equation, with the surface tension effect taken into consideration. Due to the unknown boundary and surface tension effect, this problem is an essentially nonlinear problem. By following a functional analytical approach and the theory of maximal regularity, we prove that solutions of this free boundary problem are real analytic in time and space for any positive time, even if the given initial data admit mild regularity only.