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

TL;DR

This paper provides an elementary yet rigorous overview of viscosity solutions for fully nonlinear second-order PDEs, emphasizing their applications to the calculus of variations in the $L^ Infty$ space.

Contribution

It offers a clear, accessible introduction to viscosity solutions and demonstrates their relevance to variational problems in $L^ Infty$, bridging theory and applications.

Findings

Rigorous presentation of viscosity solutions fundamentals

Application to calculus of variations in $L^ Infty$

Establishment of foundational concepts for further research

Abstract

The purpose of these expository notes is to give a quick and elementary, yet rigorous, presentation of the rudiments of the theory of Viscosity Solutions for fully nonlinear 2nd order PDE, with applications to Calculus of Variations in the space $L^\infty$.