Nonlocal Diffusion and Applications

Nonfiction, Science & Nature, Mathematics, Differential Equations, Calculus
Cover of the book Nonlocal Diffusion and Applications by Enrico Valdinoci, Claudia Bucur, Springer International Publishing
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Author: Enrico Valdinoci, Claudia Bucur ISBN: 9783319287393
Publisher: Springer International Publishing Publication: April 8, 2016
Imprint: Springer Language: English
Author: Enrico Valdinoci, Claudia Bucur
ISBN: 9783319287393
Publisher: Springer International Publishing
Publication: April 8, 2016
Imprint: Springer
Language: English

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.

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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.

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