Inserted: 1 dec 2005
Last Updated: 6 sep 2007
Journal: Commun. Pure Appl. Anal.
We prove some comparison principles for viscosity solutions of fully nonlinear degenerate elliptic equations that satisfy conditions of partial non-degeneracy instead of the usual uniform ellipticity or strict monotonicity. These results are applied to the well-posedness of the Dirichlet problem under suitable conditions at the characteristic points of the boundary. The examples motivating the theory are operators of the form of sum of squares of vector fields plus a nonlinear first order Hamiltonian and the Pucci operator over the Heisenberg group.
Keywords: Viscosity solutions, subelliptic equations, Comparison principle, Pucci operators