Regularity of the free boundary in a two-phase semilinear problem in two dimensions
Erik Lindgren, Arshak Petrosyan · Indiana University Mathematics Journal · 2008
+) p + λ−(u − ) p) ´ dx for p ∈ (0, 1) without any sign restriction on the function u. The main result states that in dimension two the free boundaries Γ + = ∂{u> 0} ∩ D and Γ − = ∂{u < 0} ∩ D are C1-regular.