Fully Nonlinear Equations

In this chapter, we develop the theory of fully nonlinear nonlocal elliptic equations. We begin with the definition of viscosity solutions and their existence and then prove the Harnack inequality and Hölder estimates for equations with “bounded measurable coefficients.” After that, we establish the main interior regularity estimates in both the general and the concave/convex case and conclude with a brief discussion of some open problems.