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＜E-Book＞
An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ / by Nikos Katzourakis
(SpringerBriefs in Mathematics. ISSN:21918201)

Edition	1st ed. 2015.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2015
Language	English
Size	XII, 123 p. 25 illus., 1 illus. in color : online resource
Authors	*Katzourakis, Nikos author SpringerLink (Online service)
Subjects	LCSH:Differential equations LCSH:Mathematical optimization LCSH:Calculus of variations FREE:Differential Equations FREE:Calculus of Variations and Optimization
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-319-12829-0

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