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

Record Type:	Language materials, printed : Monograph/item
Title/Author:	An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞/ by Nikos Katzourakis.
Author:	Katzourakis, Nikos.
Description:	XII, 123 p. 25 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Partial differential equations. -
Online resource:	https://doi.org/10.1007/978-3-319-12829-0
ISBN:	9783319128290

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

An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞[electronic resource] /by Nikos Katzourakis. - 1st ed. 2015. - XII, 123 p. 25 illus., 1 illus. in color.online resource. - SpringerBriefs in Mathematics,2191-8198. - 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. 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: 9783319128290

Standard No.: 10.1007/978-3-319-12829-0doiSubjects--Topical Terms:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞
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520 $a 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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