An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞ [Documento eletrónico] / Nikos Katzourakis
Language: eng.Country: Switzerland, Swiss Confederation.Publication: Cham : Springer International Publishing, 2015Description: XII, 123 p. : il.ISBN: 978-3-319-12829-0.Series: SpringerBriefs in MathematicsSubject - Topical Name: 3647 | 5098Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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E-Books | Biblioteca NOVA FCT Online | Não Ficção | QA374.SPR FCT 96654 (Browse shelf(Opens below)) | 1 | Available |
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QA374.SPR FCT 96472 Evolution equations of von Karman type | QA374.SPR FCT 96539 Applied partial differential equations | QA374.SPR FCT 96587 Solutions of nonlinear Schrӧdinger systems | QA374.SPR FCT 96654 An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞ | QA374.SPR FCT 96714 Evolution PDEs with nonstandard growth conditions, existence, uniqueness, localization, blow-up | QA374.SPR FCT 96734 From particle systems to partial differential equations II, particle systems and PDEs II, Braga, Portugal, December 2013 | QA374.SPR FCT 96804 Elliptic–hyperbolic partial differential equations, a mini-course in geometric and quasilinear methods |
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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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