Contemporary research in elliptic PDEs and related topics. ([2019])

• Record Type: Book
• Further Information: Note: Editor Serena Dipierro.
• Editors: Dipierro, Serena
• Contents: Intro; Preface; Contents; About the Editor; Getting Acquainted with the Fractional Laplacian; 1 The Laplace Operator; 2 Some Fractional Operators; 2.1 The Fractional Laplacian; 2.2 The Regional (or Censored) Fractional Laplacian; 2.3 The Spectral Fractional Laplacian; 2.4 Fractional Time Derivatives; 3 A More General Point of View: The ``Master Equation''; 4 Probabilistic Motivations; 4.1 The Heat Equation and the Classical Laplacian; 4.2 The Fractional Laplacian and the Regional Fractional Laplacian; 4.3 The Spectral Fractional Laplacian; 4.4 Fractional Time Derivatives 4.5 Fractional Time Diffusion Arising from Heterogeneous Media5 All Functions Are Locally s-Caloric (Up to a Small Error): Proof of (2.12); Appendix A: Confirmation of (2.7); Appendix B: Proof of (2.10); Appendix C: Proof of (2.14); Appendix D: Proof of (2.17); Appendix E: Deducing (2.19) from (2.15) Using a Space Inversion; Appendix F: Proof of (2.21); Appendix G: Proof of (2.24) and Probabilistic Insights; Appendix H: Another Proof of (2.24); Appendix I: Proof of (2.29) (Based on Fourier Methods); Appendix J: Another Proof of (2.29) (Based on Extension Methods); Appendix K: Proof of (2.36) Appendix L: Proof of (2.38)Appendix M: Another Proof of (2.38) (Based on (2.29)); Appendix N: Proof of (2.46); Appendix O: Proof of (2.48); Appendix P: Proof of (2.52); Appendix Q: Proof of (2.53); Appendix R: Proof of (2.54); Appendix S: Proof of (2.60); Appendix T: Proof of (2.61); Appendix U: Proof of (2.62); Appendix V: Memory Effects of Caputo Type; Appendix W: Proof of (3.7); Appendix X: Proof of (3.12); References; Dirichlet Problems for Fully Nonlinear Equations with ``Subquadratic'' Hamiltonians; 1 Content of the Paper; 2 Lipschitz Estimates 3 Existence and Uniqueness Results for Homogenous Dirichlet Conditions4 Non Homogeneous Boundary Conditions; References; Monotonicity Formulas for Static Metrics with Non-zero Cosmological Constant; 1 Introduction; 1.1 Static Einstein System; 1.2 Setting of the Problem and Statement of the Main Results (Case > 0); 1.3 Setting of the Problem and Statement of the Main Results (Case 0); 2.2 The Geometry of M (Case > 0) 2.3 Consequences on a Generic Level Set of u (Case 0); 3.2 A Conformal Change of Metric (Case 0: Theorem 3.2 Implies Theorem 1.1; 4.2 Case < 0: Theorem 3.2 Implies Theorem 1.4; 5 Integral Identities; 5.1 First Integral Identity; 5.2 Second Integral Identity
• Publisher Details: Cham : Springer
• Publication Date: 2019
• Copyright Date: 2019
• Extent: 1 online resource, illustrations
• Subjects: 515/.3533; Differential equations, Elliptic; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030189211
• Related ISBNs: 303018921X; 9783030189204
• Notes: Note: Includes bibliographical references.; Note: Online resource ; title from PDF title page (EBSCO, viewed July 16, 2019).
• 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.