Two-phase problems with distributed source: regularity of the free boundary
arXiv:1210.7226 · doi:10.2140/apde.2014.7.267
Abstract
We investigate the regularity of the free boundary for a general class of two-phase free boundary problems with non-zero right hand side. We prove that Lipschitz or flat free boundaries are $C^{1,γ}$. In particular, viscosity solutions are indeed classical.