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An introduction to viscosity solutio...

Katzourakis, Nikos.

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An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L [Infinite]

Record Type:	Electronic resources : Monograph/item
Title/Author:	An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L [Infinite]/ by Nikos Katzourakis.
remainder title:	An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L
Author:	Katzourakis, Nikos.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xii, 123 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Differential equations, Partial. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-12829-0
ISBN:	9783319128290 (electronic bk.)

An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L [Infinite]
Katzourakis, Nikos.

An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L [Infinite][electronic resource] /An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in Lby Nikos Katzourakis. - Cham :Springer International Publishing :2015. - xii, 123 p. :ill. (some col.), digital ;24 cm. - 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 (electronic bk.)

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

518115
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L [Infinite]
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020 $a 9783319128290 (electronic bk.)
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100 1 $a Katzourakis, Nikos. $3 2132170
245 1 3 $a An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L [Infinite] $h [electronic resource] / $c by Nikos Katzourakis.
246 3 $a An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xii, 123 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
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.
650 0 $a Differential equations, Partial. $3 518115
650 0 $a Differential equations, Nonlinear. $3 604084
650 0 $a Calculus of variations. $3 516604
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 898674
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematics. $3 1566700
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-12829-0
950 $a Mathematics and Statistics (Springer-11649)