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

Nikos Katzourakis

ISBN 10: 3319128280 / ISBN 13: 9783319128283

Editore: Springer International Publishing AG, CH, 2014

Riguardo questo articolo

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.

Codice articolo LU-9783319128283

Dati bibliografici

• Titolo: An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L?
• Editore: Springer International Publishing AG, CH
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 3319128280
• ISBN 13: 9783319128283
• Rilegatura: Paperback
• Edizione: 2015 ed.
• Condizione: New

Descrizione articolo

Riassunto

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.