Existence Results for Nonproper Elliptic Equations Involving the Pucci Operator

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Symmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations (2007, methodology): “We are going to show that the moving planes method of Alexandrov [1] and Serrin [23], in its version developed in [7], can actually be adapted to work in the setting of viscosity solutions and general equations (1.1).”
Solvability of Uniformly Elliptic Fully Nonlinear PDE (2010, unknown): “Note Leray-Schauder degree theory was shown to apply to fully nonlinear equations in [QS2].”
Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space (2015, background): “For more general operators, similar problem for equations and systems have been studied by the Quaas and Sirakov [24,25] and reference therein for other related results.”