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Nonlocal Diffusion and Applications
Claudia BucurEnrico Valdinoci
出版Springer, 2016-04-08
主題Mathematics / Differential Equations / GeneralMathematics / OptimizationMathematics / Mathematical AnalysisMathematics / Functional AnalysisMathematics / Calculus
ISBN33192873979783319287393
URLhttp://books.google.com.hk/books?id=1dv7CwAAQBAJ&hl=&source=gbs_api
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註釋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.