Special Session 47: Singular limits in elliptic and parabolic PDEs

Degenerate elliptic equations with nonlinear Hamiltonians: existence results

Isabeau Birindelli
Sapienza Università di Roma
Co-Author(s):    Galise, Rodriguez
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 Monge-Amp\`ere operator.