An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞. (2015)

• Record Type: Book
• Further Information: Note: Nikos Katzourakis.
• Authors: Katzourakis, Nikos
• Contents: 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.
• Publisher Details: Cham : Springer
• Publication Date: 2015
• Extent: 1 online resource (xii, 123 pages), illustrations (some color)
• Subjects: 515/.353; 510; Mathematics; Differential equations, Partial; Differential equations, Nonlinear; Calculus of variations; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization; Calculus of variations; Differential equations, Nonlinear; Differential equations, Partial; Mathematics; Mathematics -- Calculus; Calculus of variations; Mathematical optimization; Mathematics -- Differential Equations; Differential calculus & equations; Electronic books
• Languages: English
• ISBNs: 9783319128290; 3319128299
• Related ISBNs: 9783319128283; 3319128280
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed February 3, 2015).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.