We examine a free transmission problem driven by fully nonlinear elliptic operators. Since the transmission interface is determined endogenously, our analysis regards this object as a free boundary. We start by relating our problem with a pair of viscosity inequalities. Then, approximation methods ensure that strong solutions are of class , locally. In addition, under further conditions on the problem, we prove quadratic growth of the solutions away from branch points.
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Edgard A. Pimentel, Makson S. Santos, Fully nonlinear free transmission problems. Interfaces Free Bound. 25 (2023), no. 3, pp. 325–342DOI 10.4171/IFB/489