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CPAA

We prove a comparison principle for viscosity solutions of a fully nonlinear equation
satisfying a condition of non-degeneracy in a fixed direction.
We apply these results
to prove that a continuous solution
of the corresponding Dirichlet problem exists.
To obtain the existence of barrier functions and well-posedness, we find suitable explicit assumptions on the domain and on the ellipticity constants of the operator.

CPAA

We prove some comparison principles for viscosity solutions of fully nonlinear degenerate elliptic equations
that satisfy some 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.

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