عنوان

Contemporary research in elliptic PDEs and related topics /

303018921X

9783030189211

9783030189204

Contemporary research in elliptic PDEs and related topics /

[Book]

editor Serena Dipierro.

Cham :

Springer,

[2019]

©2019

1 online resource :

illustrations

Springer INdAM series ;

volume 33

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 ``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

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

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)

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

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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.

Springer Nature

com.springer.onix.9783030189211

Differential equations, Elliptic.

Differential equations, Elliptic.

Dipierro, Serena

20200823090556.0

pn

[Book]

Y