  Most of lipschitz regularity results for nonlinear strictly elliptic
equations are obtained for a suitable growth power of the nonlinearity with
respect to the gradient variable (subquadratic for instance). For equations
with superquadratic growth power in gradient, one usually uses weak
Bernstein-type arguments which require regularity and/or convex-type
assumptions on the gradient nonlinearity. In this article, we obtain new
Lipschitz regularity results for a large class of nonlinear strictly elliptic
equations with possibly arbitrary growth power of the Hamiltonian with respect
to the gradient variable using some ideas coming from Ishii-Lions' method. We
use these bounds to solve an ergodic problem and to study the regularity and
the large time behavior of the solution of the evolution equation.
