Nonlocal Diffusion and Applications

  • Claudia Bucur
  • Enrico Valdinoci

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Claudia Bucur, Enrico Valdinoci
    Pages 1-5
  3. Claudia Bucur, Enrico Valdinoci
    Pages 7-37
  4. Claudia Bucur, Enrico Valdinoci
    Pages 39-65
  5. Claudia Bucur, Enrico Valdinoci
    Pages 67-95
  6. Claudia Bucur, Enrico Valdinoci
    Pages 97-126
  7. Claudia Bucur, Enrico Valdinoci
    Pages 127-138
  8. Back Matter
    Pages 139-157

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.


35S05; 47G10; 35S30; 47B34; 35R11; 49Q05; 82D25; 74E15; 35Q40. Fractional diffusion Fractional Laplacian Nonlocal minimal surfaces Nonlocal phase transitions Nonlocal quantum mechanics

Authors and affiliations

  • Claudia Bucur
    • 1
  • Enrico Valdinoci
    • 2
  1. 1.DipartimentodiMatematicaFederigoEnriquesUniversità degli Studi di MilanoMilanoItaly
  2. 2.DipartimentodiMatematicaFederigoEnriquesUniversità degli Studi di MilanoMilanoItaly

Bibliographic information