Regularity of the solution and of the free boundary for free boundary problems arising in combustion theory (Q1570420)

The problem under consideration is a two-phase free boundary problem for the heat equation, where on the free boundary a relation of the type \[ G((x,t),{\nu}, u^+_{\nu}, u^-{\nu})=1R \] besides \(u=0\) is given. This relation generalizes the cases \(u_{\nu}=1\) and \((u^+_{\nu}-u^-{\nu}=M (M>0))\). The author proves, that Lipschitz free boundaries in space and time are \(C^{1,\beta}\) in space and \(C^{1,\beta /2}\) in time and that viscosity solutions are indeed classical ones.