An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞
Author | : Nikos Katzourakis |
Publisher | : Springer |
Total Pages | : 125 |
Release | : 2014-11-26 |
ISBN-10 | : 9783319128290 |
ISBN-13 | : 3319128299 |
Rating | : 4/5 (299 Downloads) |
Download or read book An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ written by Nikos Katzourakis and published by Springer. This book was released on 2014-11-26 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.