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The Dirichlet problem for fully nonlinear elliptic equations non-degenerate in a fixed direction

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  • 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.
    Mathematics Subject Classification: 35J70, 35H20, 35J60.


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