Nonlocal diffusion and applications

2015/04/30 by Claudia Bucur, Enrico Valdinoci · 2 citations
Mathematics · #math.AP

paper · pdf · doi:10.1007/978-3-319-28739-3

published as Lecture Notes of the Unione Matematica Italiana, v. 20, Springer 2016 · 132 pages, 26 figures

arxiv created 2018/04/27 · arxiv updated 2018/04/30

Abstract

We consider the fractional Laplace framework and provide models and theorems related to nonlocal diffusion phenomena. Some applications are presented, including: a simple probabilistic interpretation, water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations. Furthermore, an example of an s-harmonic function, the harmonic extension and some insight on a fractional version of a classical conjecture formulated by De Giorgi are presented. Although this book aims at gathering some introductory material on the applications of the fractional Laplacian, some proofs and results are original. Also, the work is self contained, and the reader is invited to consult the rich bibliography for further details, whenever a subject is of interest.

Cited by

• Dynamics of Fractional Wave Equations with Nonlocal Damping
• Local Boundedness of a Direction Dependent Double Phase Nonlocal Elliptic Equation

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