Contemporary research in elliptic PDEs and related topics
This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applic...
| Other Authors: | Dipierro, Serena,, SpringerLink (Online service) |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer,
[2019]
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| Physical Description: |
1 online resource : illustrations. |
| Series: |
Springer INdAM series ;
v. 33. |
| Subjects: |
| Summary: |
This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research. |
|---|---|
| Item Description: |
Includes bibliographical references. 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 M̀̀aster 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 S̀̀ubquadratic'' 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. This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research. |
| Physical Description: |
1 online resource : illustrations. |
| Bibliography: |
Includes bibliographical references. |
| ISBN: |
9783030189211 303018921X |