An Introduction to Viscosity Solutions for Fully Nonlinear Pde with Applications to Calculus of Variations in L∞

By Nikos Katzourakis

The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a weak solution do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using integration-by-parts in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.

• Format: Paperback
• Language: English
• ISBN: 3319128280
• ISBN13: 9783319128283
• Release Date: December 2014
• Publisher: Springer
• Length: 123 Pages
• Weight: 0.44 lbs.
• Dimensions: 0.3" x 6.1" x 9.2"