Nonlocal diffusion and applications. (2016)

• Record Type: Book
• Further Information: Note: Claudia Bucur, Enrico Valdinoci.
• Authors: Bucur, Claudia; Valdinoci, Enrico, 1974-
• Contents: Introduction -- 1 A probabilistic motivation.-1.1 The random walk with arbitrarily long jumps -- 1.2 A payoff model.-2 An introduction to the fractional Laplacian.-2.1 Preliminary notions -- 2.2 Fractional Sobolev Inequality and Generalized Coarea Formula -- 2.3 Maximum Principle and Harnack Inequality -- 2.4 An s-harmonic function -- 2.5 All functions are locally s-harmonic up to a small error -- 2.6 A function with constant fractional Laplacian on the ball -- 3 Extension problems -- 3.1 Water wave model -- 3.2 Crystal dislocation -- 3.3 An approach to the extension problem via the Fourier transform -- 4 Nonlocal phase transitions -- 4.1 The fractional Allen-Cahn equation -- 4.2 A nonlocal version of a conjecture by De Giorgi -- 5 Nonlocal minimal surfaces -- 5.1 Graphs and s-minimal surfaces -- 5.2 Non-existence of singular cones in dimension 2 5.3 Boundary regularity -- 6 A nonlocal nonlinear stationary Schrödinger type equation -- 6.1 From the nonlocal Uncertainty Principle to a fractional weighted inequality -- Alternative proofs of some results -- A.1 Another proof of Theorem A.2 Another proof of Lemma 2.3 -- References.
• Publisher Details: Switzerland : Springer
• Publication Date: 2016
• Extent: 1 online resource (xii, 155 pages), illustrations (some color)
• Subjects: 515/.53; Mathematics; Harmonic functions; Laplace transformation; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Harmonic functions; Laplace transformation; Mathematics -- Mathematical Analysis; Mathematics -- Functional Analysis; Calculus of variations; Integral calculus & equations; Functional analysis & transforms; Differential equations, partial; Mathematical optimization; Integral Transforms; Functional analysis; Mathematics -- Differential Equations; Differential calculus & equations; Electronic books
• Languages: English
• ISBNs: 9783319287393; 3319287397; 3319287389; 9783319287386
• Related ISBNs: 9783319287386
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed April 12, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.