SpringerBriefs in Mathematics

Katzourakis, Nikos

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.

Details

Published by: Springer

Publication Date: 2014-12-10

Format: Paperback

ISBN-13: 9783319128283

DOI: 10.1007/978-3-319-12829-0

Dimensions: 235cm x155cm

Pages: 123