Regularity for nonisotropic two-phase problems with Lipschitz free boundaries
A two-phase free boundary value problem is studied in which the positive and negative parts of the solution satisfy two different elliptic equations. It is shown that if the free boundary (between both parts) is locally Lipschitz, then it is \(C^{1,\alpha}\) smooth. This extends a result of \textit{L. A. Caffarelli} [Rev. Mat. Iberoam. 3, 139-162 (1987; Zbl 0676.35085)] where the positive and negative parts satisfy the same equation.
scientific article; zbMATH DE number 1450176