Argiolas, Roberto; Ferrari, Fausto Flat free boundaries regularity in two-phase problems for a class of fully nonlinear elliptic operators with variable coefficients. (English) Zbl 1179.35349 Interfaces Free Bound. 11, No. 2, 177-199 (2009). The author consider the following free boundary problem: \[ \begin{cases} F(D^2u(x),x)=0 &\text{in }\Omega^+(u)=\{x\in \Omega\subset \mathbb R^n:\;u>0\},\\ F(D^2u(x),x)=0 &\text{in }\Omega^-(u)=\{x\in \Omega\subset \mathbb R^n:\;u\leq 0\},\\ u=0&\text{on }\partial\Omega^+\cap\Omega,\\ u_\nu^+=G(u_\nu^-)=0&\text{on }\partial\Omega^+\cap\Omega,\end{cases} \] where \(u\) is a viscosity solution of the equation \(F(D^2u(x),x)=0\). It is proved that flat free boundaries are \(C^{1,\gamma}\). Reviewer: Nikolai V. Krasnoschok (Donetsk) Cited in 12 Documents MSC: 35R35 Free boundary problems for PDEs 35B65 Smoothness and regularity of solutions to PDEs Keywords:free boundary; two-phase problem; weak monotonicity PDFBibTeX XMLCite \textit{R. Argiolas} and \textit{F. Ferrari}, Interfaces Free Bound. 11, No. 2, 177--199 (2009; Zbl 1179.35349) Full Text: DOI Link