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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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Lenguaje: | eng |
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Springer
2015
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Acceso en línea: | https://dx.doi.org/10.1007/978-3-319-12829-0 http://cds.cern.ch/record/1973528 |
_version_ | 1780944946350522368 |
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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. |
id | cern-1973528 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2015 |
publisher | Springer |
record_format | invenio |
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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