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Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE

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  • Two results are proved in the paper. The first is a uniqueness theorem for viscosity solutions of Dirichlet boundary value problems for Bellman-Isaacs equations with just measurable lower order terms. The second is a proof that there always exist maximal and minimal viscosity solutions of Dirichlet boundary value problems for fully nonlinear, uniformly elliptic PDE that are measurable in the $x$-variable.
    Mathematics Subject Classification: 35J60, 35J65, 35J25, 49L25.

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