Viscosity Solutions: An Introduction to the basics of the theory

Official URL: http://risc01.sabanciuniv.edu/record=b1064371 (Table of Contents)

In this work, concepts that appear in the basic theory of viscosity solutions theory is surveyed. Structures of sub and super di.erentials and sub and super semijets, and concepts of generalized second derivative, generalized 'maximum principle' and generalized 'comparison principle' are studied. Basic properties of semiconvex functions and sup (Jensen's) convolutions are presented. Existence and uniqueness of solutions of the Dirichlet Problem for first and second order nonlinear elliptic partial differential equations is studied.