Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampère equations : VIASM 2016 /: VIASM 2016. (2017)

• Record Type: Book
• Further Information: Note: Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran.
• Authors: Lê, Nam Q; Mitake, Hiroyoshi; Tran, Hung V
• Editors: Mitake, Hiroyoshi; Tran, Hung V
• Contents: Intro; Preface; Contents; Part I The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation and Related Linearized Monge-Ampère Equation; Introduction; Notation; 1 The Affine Bernstein and Boundary Value Problems; 1.1 The Affine Bernstein and Boundary Value Problems; 1.1.1 Minimal Graph; 1.1.2 Affine Maximal Graph; 1.1.3 The Affine Bernstein Problem; 1.1.4 Connection with the Constant Scalar Curvature Problem; 1.1.5 The First Boundary Value Problem; 1.1.6 The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation 2.1 The Linearized Monge-Ampère Equation and Interior Regularity of Its Solution2.1.1 The Linearized Monge-Ampère Equation; 2.1.2 Linearized Monge-Ampère Equations in Contexts; 2.1.3 Difficulties and Expected Regularity; 2.1.4 Affine Invariance Property; 2.1.5 Krylov-Safonov's Harnack Inequality; 2.1.6 Harnack Inequality for the Linearized Monge-Ampère Equation; 2.2 Interior Harnack and Hölder Estimates for Linearized Monge-Ampère; 2.2.1 Proof of Caffarelli-Gutiérrez's Harnack Inequality; 2.2.2 Proof of the Interior Hölder Estimates for the Inhomogeneous Linearized Monge-Ampère Equation 2.3 Global Hölder Estimates for the Linearized Monge-Ampère Equations2.3.1 Boundary Hölder Continuity for Solutions of Non-uniformly Elliptic Equations; 2.3.2 Savin's Localization Theorem; 2.3.3 Proof of Global Hölder Estimates for the Linearized Monge-Ampère Equation; References; 3 The Monge-Ampère Equation; 3.1 Maximum Principles and Sections of the Monge-Ampère Equation; 3.1.1 Basic Definitions; 3.1.2 Examples and Properties of the Normal Mapping and the Monge-Ampère Measure; 3.1.3 Maximum Principles; 3.1.4 John's Lemma; 3.1.5 Comparison Principle and Applications
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource (vii, 228 pages), illustrations (some color)
• Subjects: 515/.353; Mathematics; Hamilton-Jacobi equations -- Congresses; Monge-Ampère equations -- Congresses; Differential equations, partial; Mathematical optimization; Global differential geometry; Hamilton-Jacobi equations; Monge-Ampère equations; Mathematics -- Calculus; Mathematics -- Geometry -- Differential; Calculus of variations; Differential & Riemannian geometry; Mathematics -- Differential Equations; Differential calculus & equations; Mathematics; Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization; Differential Geometry; Electronic books; Conference papers and proceedings
• Languages: English
• ISBNs: 9783319542089; 3319542087; 3319542079; 9783319542072
• Related ISBNs: 9783319542072
• Notes: Note: Online resource; title from PDF title page (SpringerLink, viewed June 21, 2017).
• 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.