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

Katzourakis, Nikos

Couverture souple

ISBN 10 : 3319128280 ISBN 13 : 9783319128283

Editeur : Springer, 2014

Synopsis

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2014
• Langue: anglais
• ISBN 10: 3319128280
• ISBN 13: 9783319128283
• Reliure: Broché
• Nombre de pages: 136
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne