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|a 9783319128290
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|a Katzourakis, Nikos
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| 245 |
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|a An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞
|h Elektronische Ressource
|c by Nikos Katzourakis
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| 250 |
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|a 1st ed. 2015
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| 260 |
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|a Cham
|b Springer International Publishing
|c 2015, 2015
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| 300 |
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|a XII, 123 p. 25 illus., 1 illus. in color
|b online resource
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| 653 |
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|a Calculus of Variations and Optimization
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| 653 |
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|a Mathematical optimization
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| 653 |
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|a Differential Equations
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| 653 |
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|a Differential equations
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| 653 |
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|a Calculus of variations
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a SpringerBriefs in Mathematics
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| 028 |
5 |
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|a 10.1007/978-3-319-12829-0
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| 856 |
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|u https://doi.org/10.1007/978-3-319-12829-0?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 515.35
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| 520 |
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|a 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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