000754762 000__ 03823cam\a2200493Ii\4500
000754762 001__ 754762
000754762 005__ 20230306141725.0
000754762 006__ m\\\\\o\\d\\\\\\\\
000754762 007__ cr\cn\nnnunnun
000754762 008__ 160412s2016\\\\sz\a\\\\ob\\\\000\0\eng\d
000754762 019__ $$a946706178$$a946788301
000754762 020__ $$a9783319287393$$q(electronic book)
000754762 020__ $$a3319287397$$q(electronic book)
000754762 020__ $$z9783319287386
000754762 0247_ $$a10.1007/978-3-319-28739-3$$2doi
000754762 035__ $$aSP(OCoLC)ocn946520853
000754762 035__ $$aSP(OCoLC)946520853$$z(OCoLC)946706178$$z(OCoLC)946788301
000754762 037__ $$a913380$$bMIL
000754762 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dGW5XE$$dYDXCP$$dN$T$$dAZU$$dOCLCF$$dCDX$$dCOO$$dEBLCP$$dIDEBK
000754762 049__ $$aISEA
000754762 050_4 $$aQA405
000754762 08204 $$a515/.53$$223
000754762 1001_ $$aBucur, Claudia,$$eauthor.
000754762 24510 $$aNonlocal diffusion and applications$$h[electronic resource] /$$cClaudia Bucur, Enrico Valdinoci.
000754762 264_1 $$aSwitzerland :$$bSpringer,$$c2016.
000754762 300__ $$a1 online resource (xii, 155 pages) :$$billustrations.
000754762 336__ $$atext$$btxt$$2rdacontent
000754762 337__ $$acomputer$$bc$$2rdamedia
000754762 338__ $$aonline resource$$bcr$$2rdacarrier
000754762 4901_ $$aLecture notes of the Unione Matematica Italiana,$$x1862-9113 ;$$v20
000754762 504__ $$aIncludes bibliographical references.
000754762 5050_ $$aIntroduction -- 1 A probabilistic motivation.-1.1 The random walk with arbitrarily long jumps -- 1.2 A payoff model.-2 An introduction to the fractional Laplacian.-2.1 Preliminary notions -- 2.2 Fractional Sobolev Inequality and Generalized Coarea Formula -- 2.3 Maximum Principle and Harnack Inequality -- 2.4 An s-harmonic function -- 2.5 All functions are locally s-harmonic up to a small error -- 2.6 A function with constant fractional Laplacian on the ball -- 3 Extension problems -- 3.1 Water wave model -- 3.2 Crystal dislocation -- 3.3 An approach to the extension problem via the Fourier transform -- 4 Nonlocal phase transitions -- 4.1 The fractional Allen-Cahn equation -- 4.2 A nonlocal version of a conjecture by De Giorgi -- 5 Nonlocal minimal surfaces -- 5.1 Graphs and s-minimal surfaces -- 5.2 Non-existence of singular cones in dimension 2 5.3 Boundary regularity -- 6 A nonlocal nonlinear stationary Schrödinger type equation -- 6.1 From the nonlocal Uncertainty Principle to a fractional weighted inequality -- Alternative proofs of some results -- A.1 Another proof of Theorem A.2 Another proof of Lemma 2.3 -- References.
000754762 506__ $$aAccess limited to authorized users.
000754762 520__ $$aWorking in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.
000754762 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed April 12, 2016).
000754762 650_0 $$aHarmonic functions.
000754762 650_0 $$aLaplace transformation.
000754762 7001_ $$aValdinoci, Enrico,$$d1974-$$eauthor.
000754762 77608 $$iPrint version:$$z9783319287386
000754762 830_0 $$aLecture notes of the Unione Matematica Italiana ;$$v20.
000754762 852__ $$bebk
000754762 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-28739-3$$zOnline Access$$91397441.1
000754762 909CO $$ooai:library.usi.edu:754762$$pGLOBAL_SET
000754762 980__ $$aEBOOK
000754762 980__ $$aBIB
000754762 982__ $$aEbook
000754762 983__ $$aOnline
000754762 994__ $$a92$$bISE