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

von Nikos Katzourakis

123 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: SpringerBriefs in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Mathematische Analysis, allgemein Differentialrechnung und -gleichungen
• ISBN: 9783319128283
• Sprache: Englisch
• Erscheinungsdatum: 10.12.2014
• Größe: 23.5 x 15.5 cm
• Verlag: Springer International Publishing