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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| Format: | eBook |
| Langue: | English |
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Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Collection: | SpringerBriefs in Mathematics,
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| Accès en ligne: | Click here to view the full text content |
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| Résumé: | 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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| Description matérielle: | 1 online resource (xii, 123 pages) 25 illustrations, 1 illustrations in color |
| ISBN: | 9783319128290 |
| ISSN: | 2191-8198 |