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An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L

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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http://schema.org/description

  • "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."@en

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  • "Electronic books"@en
  • "Electronic books"

http://schema.org/name

  • "An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L"@en
  • "An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L"
  • "An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞"@en
  • "An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞"
  • "An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞ [L infinity]"
  • "An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in Lā„“Ģā„“"@en