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

  • Nikos Katzourakis

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

About this book

Introduction

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.

Keywords

Calculus of variations Elliptic PDEs Game theory Geometric evolution Viscosity solutions

Authors and affiliations

  • Nikos Katzourakis
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of ReadingReadingUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-12829-0
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-12828-3
  • Online ISBN 978-3-319-12829-0
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site