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An Introduction To Viscosity Solutions For Fully Nonlinear Pde With Applications To Calculus Of Variations In L(2015th Edition)

Authors:

Nikos Katzourakis

an introduction to viscosity solutions for fully nonlinear pde with applications to calculus of variations in

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Book details

ISBN: 3319128280, 978-3319128283

Book publisher: Springer

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Book Summary: 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.

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