Abstract: 
In this talk we will present existence results for degenerate elliptic equations with a nonlinear gradient term of the form
$F(x,D^2u) + H(Du) = f(x).$
in bounded uniformly convex domains $\Omega$. I willpresent sufficient conditions for the existence and uniqueness of solutions in terms of the size of $\Omega$, of the forcing term $f$ and of $H$. The results apply to a wide class of equations, since very little is required from the principal part i.e. the degenerate elliptic operators. In particular the operator could be linear, or a weighted partial trace operators or e.g. the homogeneous MongeAmp\`ere operator. 
