Regularity of the free boundary for a parabolic cooperative system

Abstract

In this paper we study the following parabolic systemwith free boundary ∂{|u| > 0}. For 0 ≤ q < 1, we prove optimal growth rate for solutions u to the above system near free boundary points, and show that in a uniform neighbourhood of any a priori well-behaved free boundary point the free boundary is C 1,α in space directions and half-Lipschitz in the time direction.