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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, solutio...

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Detalles Bibliográficos
Autor principal: Katzourakis, Nikos
Lenguaje:eng
Publicado: Springer 2015
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-12829-0
http://cds.cern.ch/record/1973528
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author Katzourakis, Nikos
author_facet Katzourakis, Nikos
author_sort Katzourakis, Nikos
collection CERN
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.
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institution Organización Europea para la Investigación Nuclear
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spelling cern-19735282021-04-21T20:41:40Zdoi:10.1007/978-3-319-12829-0http://cds.cern.ch/record/1973528engKatzourakis, NikosAn introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in l∞Mathematical Physics and MathematicsThe 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.Springeroai:cds.cern.ch:19735282015
spellingShingle Mathematical Physics and Mathematics
Katzourakis, Nikos
An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in l∞
title An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in l∞
title_full An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in l∞
title_fullStr An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in l∞
title_full_unstemmed An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in l∞
title_short An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in l∞
title_sort introduction to viscosity solutions for fully nonlinear pde with applications to calculus of variations in l∞
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-12829-0
http://cds.cern.ch/record/1973528
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