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.
| ISBN: | 9783319128283 |
| Publication date: | 10th December 2014 |
| Author: | Nikos Katzourakis |
| Publisher: | Springer an imprint of Springer International Publishing |
| Format: | Paperback |
| Pagination: | 123 pages |
| Series: | SpringerBriefs in Mathematics |
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.
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An Introduction To Viscosity Solutions for Fully Nonlinear PDE With Applications to Calculus of Variations in L8 was written by Nikos Katzourakis and published by Springer an imprint of Springer International Publishing
An Introduction To Viscosity Solutions for Fully Nonlinear PDE With Applications to Calculus of Variations in L8 has 123 pages
Yes it is part of SpringerBriefs in Mathematics series