An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞ /

An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞ /

Saved in:

Bibliographic Details
Author / Creator:	Katzourakis, Nikos, author.
Imprint:	Cham : Springer, 2015.
Description:	1 online resource (xii, 123 pages) : illustrations (some color).
Language:	English
Series:	SpringerBriefs in Mathematics, 2191-8198 SpringerBriefs in mathematics.
Subject:	Differential equations, Partial. Differential equations, Nonlinear. Calculus of variations. Calculus of variations. Differential equations, Nonlinear. Differential equations, Partial. Mathematics. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11090159

Hidden Bibliographic Details
ISBN:	9783319128290 3319128299 9783319128283 3319128280
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references. Online resource; title from PDF title page (SpringerLink, viewed February 3, 2015).
Summary:	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.
Other form:	Original 3319128280 9783319128283
Standard no.:	10.1007/978-3-319-12829-0

Description
Summary:	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.
Physical Description:	1 online resource (xii, 123 pages) : illustrations (some color).
Bibliography:	Includes bibliographical references.
ISBN:	9783319128290 3319128299 9783319128283 3319128280
ISSN:	2191-8198