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Autore: | Katzourakis Nikos |

Titolo: | An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ [[electronic resource] /] / by Nikos Katzourakis |

Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |

Edizione: | 1st ed. 2015. |

Descrizione fisica: | 1 online resource (125 p.) |

Disciplina: | 510 |

515.353 | |

515.64 | |

Soggetto topico: | Partial differential equations |

Calculus of variations | |

Partial Differential Equations | |

Calculus of Variations and Optimal Control; Optimization | |

Note generali: | Description based upon print version of record. |

Nota di bibliografia: | Includes bibliographical references. |

Nota di contenuto: | 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 |

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 | |

9.1.5 Nonlinear Boundary Conditions9.1.6 Comparison Principle for Viscosity Solutions Without Decoupling in the x-variable; References | |

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. |

Titolo autorizzato: | Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ |

ISBN: | 3-319-12829-9 |

Formato: | Materiale a stampa |

Livello bibliografico | Monografia |

Lingua di pubblicazione: | Inglese |

Record Nr.: | 9910299787703321 |

Lo trovi qui: | Univ. Federico II |

Opac: | Controlla la disponibilità qui |

Serie:
SpringerBriefs in Mathematics, . 2191-8198