Free boundary problems for second order parabolic equations (Q2761484)

This is paper devoted to the time-local classical solvability of the two-phase Stefan problem and the Muskat-Verigin problem. The authors prove classical solvability of the considered free boundary problems for domains with \(C^{2+a}\)-smooth boundaries of arbitrary shape and for minimal-order compatibility of the initial data with the boundary conditions. The solutions are obtained with maximal regularity, i.e., at an arbitrary moment of time \(t>0\) they are at least as regular as at the initial moment.