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Nonlocal Diffusion and Applications

  • Book
  • © 2016

Overview

Authors:
  1. Claudia Bucur

    1. DipartimentodiMatematicaFederigoEnriques, Università degli Studi di Milano, Milano, Italy

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  2. Enrico Valdinoci

    1. DipartimentodiMatematicaFederigoEnriques, Università degli Studi di Milano, Milano, Italy

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    You can also search for this author in PubMed   Google Scholar

  • Gives a rich introduction to the fractional Laplacian and its applications
  • Well explained, self-contained and easy to follow, even for those who are not familiar with the subject
  • Contains brand new and interesting research trends on the fractional Laplacian
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes of the Unione Matematica Italiana (UMILN, volume 20)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xii
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  2. A Probabilistic Motivation

    • Claudia Bucur, Enrico Valdinoci
    Pages 1-5

  3. An Introduction to the Fractional Laplacian

    • Claudia Bucur, Enrico Valdinoci
    Pages 7-37

  4. Extension Problems

    • Claudia Bucur, Enrico Valdinoci
    Pages 39-65

  5. Nonlocal Phase Transitions

    • Claudia Bucur, Enrico Valdinoci
    Pages 67-95

  6. Nonlocal Minimal Surfaces

    • Claudia Bucur, Enrico Valdinoci
    Pages 97-126

  7. A Nonlocal Nonlinear Stationary Schrödinger Type Equation

    • Claudia Bucur, Enrico Valdinoci
    Pages 127-138

  8. Back Matter

    Pages 139-157
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Keywords

About this book

Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.

Reviews

“The book under review is a result of a series of lectures given in various places throughout the world. It gives an introduction to the analysis of nonlocal operators, most notably the fractional Laplacian. … the book does a great job of introducing the topic of nonlocal analysis for every newcomer in the field. It provides a good starting point for doing research and therefore is highly recommended.” (Łukasz Płociniczak, Mathematical Reviews, March, 2017)

Authors and Affiliations

  • DipartimentodiMatematicaFederigoEnriques, Università degli Studi di Milano, Milano, Italy

    Claudia Bucur, Enrico Valdinoci

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