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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.353
書名/作者:	An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L [Infinite]/ by Nikos Katzourakis.
其他題名:	An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L
作者:	Katzourakis, Nikos.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xii, 123 p. : : ill. (some col.), digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Differential equations, Partial.
標題:	Differential equations, Nonlinear.
標題:	Calculus of variations.
標題:	Mathematics.
標題:	Partial Differential Equations.
標題:	Calculus of Variations and Optimal Control; Optimization.
ISBN:	9783319128290 (electronic bk.)
ISBN:	9783319128283 (paper)
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-12829-0

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

389324
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][electronic resource] /
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