Fully nonlinear free transmission problems with nonhomogeneous degeneracies

Abstract

We prove existence and regularity results for free transmission problems governed by fully nonlinear elliptic equations with nonhomogeneous degeneracies. 2.1. Notation 5 2.2. On uniformly elliptic operators 5 2.3. The homogeneous problem 8 2.4. Main assumptions 8 3. Existence of solutions 9 3.1. Proof of Theorem 1 13 4. Compactness for switched differential inequalities 13 5. Gradient Hölder continuity 16 5.1. Smallness regime 16 5.2. Harmonic approximation 17 5.3. Proof of Theorem 2 22 Appendix A. Hölder estimates for multi-phase equations with variable exponents 22 References 25