Titlebook: Nonlocal Diffusion and Applications; Claudia Bucur,Enrico Valdinoci Book 2016 Springer International Publishing Switzerland 2016 35S05; 47

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Claudia Bucur,Enrico ValdinociGives 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 an

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978-3-319-28738-6Springer International Publishing Switzerland 2016

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Nonlocal Diffusion and Applications978-3-319-28739-3Series ISSN 1862-9113 Series E-ISSN 1862-9121

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A Probabilistic Motivation,phenomena. We introduce briefly the fractional Laplacian and then we present two probabilistic models in which such operator naturally arises: a random walk that allows long jumps and a payoff model. Indeed, we show that the fractional heat equation (i.e. the “typical” equation that drives the fract

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An Introduction to the Fractional Laplacian, for the fractional Laplacian are introduced and the constant that appears in this definition is explicitly computed. Fractional Sobolev spaces enjoy quite a number of important functional inequalities. We will present here two important inequalities which have a simple and nice proof, namely the fr

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Extension Problems,d a model related to crystal dislocations, making clear how the extension problem appears in these models. Indeed, we show that the extension operator related to the half-Laplacian arises in the theory of water waves of irrotational, incompressible, inviscid fluids in the small amplitude, long wave

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,A Nonlocal Nonlinear Stationary Schrödinger Type Equation,quation, the Benjamin-Bona-Mahony equation and the fractional Schrödinger equation). In this chapter, only stationary equations are studied. This type of equation arises in the study of the fractional Schrödinger equation when looking for standing waves. The first section deals with the existence of

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