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[null,"1.","Record Nr.",null,"UNINA9910299787703321"]
[null,null,"Autore",null,"Katzourakis Nikos"]
[null,null,"Titolo",null,"An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ / / by Nikos Katzourakis"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015"]
[null,null,"ISBN",null,"3-319-12829-9"]
[null,null,"Edizione",null,"[1st ed. 2015.]"]
[null,null,"Descrizione fisica",null,"1 online resource (125 p.)"]
[null,null,"Collana",null,"SpringerBriefs in Mathematics, , 2191-8198"]
[null,null,"Disciplina",null,"510"]
[{"$nulls":4},"515.353"]
[{"$nulls":4},"515.64"]
[null,null,"Soggetti",null,"Differential equations, Partial"]
[{"$nulls":4},"Calculus of variations"]
[{"$nulls":4},"Partial Differential Equations"]
[{"$nulls":4},"Calculus of Variations and Optimal Control; Optimization"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references."]
[null,null,"Nota di contenuto",null,"Preface; Acknowledgments; Contents; 1 History, Examples, Motivation and First Definitions; References; 2 Second Definitions and Basic Analytic  Properties of the Notions; References; 3 Stability Properties of the Notions  and Existence via Approximation; References; 4 Mollification of Viscosity Solutions  and Semiconvexity; References; 5 Existence of Solution to the Dirichlet Problem via Perron's Method; References; 6 Comparison Results and Uniqueness of Solution to the Dirichlet Problem; References"]
[{"$nulls":4},"7 Minimisers of Convex Functionals  and Existence of Viscosity Solutions  to the Euler-Lagrange PDEReferences; 8 Existence of Viscosity Solutions to the Dirichlet Problem for the infty-Laplacian; References; 9 Miscellaneous Topics and Some  Extensions of the Theory; 9.1 Fundamental Solutions of the infty-Laplacian; 9.1.1 The infty-Laplacian and Tug-of-War Differential Games; 9.1.2 Discontinuous Coefficients, Discontinuous Solutions; 9.1.3 Barles-Perthame Relaxed Limits (1-Sided Uniform Convergence) and Generalised 1-Sided Stability; 9.1.4 Boundary Jets and Jets Relative to Non-open Sets"]
[{"$nulls":4},"9.1.5 Nonlinear Boundary Conditions9.1.6 Comparison Principle for Viscosity Solutions Without Decoupling in the x-variable; References"]
[null,null,null,"Sommario/riassunto","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."]