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The purpose of these expository notes is to give a quick and elementary, yetrigorous, presentation of the rudiments of the theory of Viscosity Solutionsfor fully nonlinear 2nd order PDE, with applications to Calculus of Variationsin the space $L^\infty$.

Lecture notes on Viscosity Solutions for fully nonlinear 2nd order PDE and applications to Calculus of Variations in $L^\infty$