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

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.

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Detail Information
Series Title
SpringerBriefs in Mathematics
Call Number
515.3 KAT i
Publisher
: Springer Cham.,
Collation
XII, 123
Language
English
ISBN/ISSN
978-3-319-12829-0
Classification
515.3
Content Type
text
Media Type
computer
Carrier Type
online resource
Edition
Ed. 1
Subject(s)
Differential equations
Calculus of Variations and Optimization
Specific Detail Info
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Statement of Responsibility
Other Information
Cataloger
umi
Source
https://link.springer.com/content/pdf/10.1007/978-3-319-12829-0.pdf?pdf=button
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