Regularity of the free boundary for some elliptic and parabolic problems. I

摘要

We study the free boundary of solutions to some obstacle problems in the elliptic and parabolic cases. In the one-phase Stefan problem, the parabolic case, we prove that the points where the zero set has no density lie in a Lipschitz surface in space and time. For some fully nonlinear elliptic equations of second order, we get similar results. Furthermore, we prove the C~1 regularity for singular points with some (n-1)-dimensional density.