Nonlocal Diffusion and Applications

Nonlocal Diffusion and Applications
Springer | Mathematics | May 10 2016 | ISBN-10: 3319287389 | 155 pages | pdf | 1.9 mb

Authors: Bucur, Claudia, Valdinoci, Enrico
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

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.

Number of Illustrations and Tables
3 b/w illustrations, 23 illustrations in colour
Partial Differential Equations
Calculus of Variations and Optimal Control; Optimization
Integral Transforms, Operational Calculus
Functional Analysis

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