An Introduction To Viscosity Solutions For Fully Nonlinear Pde With Applications To Calculus Of Var

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An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L8
By: Nikos Katzourakis
Publisher:
Springer
Print ISBN: 9783319128283, 3319128280
eText ISBN: 9783319128290, 3319128299
Copyright year: 2015
Format: EPUB
Available from $ 69.99 USD
SKU 9783319128290
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.