  This paper is concerned with H\"older regularity of viscosity solutions of
second-order, fully non-linear elliptic integro-differential equations. Our
results rely on two key ingredients: first we assume that, at each point of the
domain, either the equation is strictly elliptic in the classical fully
non-linear sense, or (and this is the most original part of our work) the
equation is strictly elliptic in a non-local non-linear sense we make precise.
Next we impose some regularity and growth conditions on the equation. These
results are concerned with a large class of integro-differential operators
whose singular measures depend on $x$ and also a large class of equations,
including Bellman-Isaacs Equations.
