TY - GEN digital ID - 131563281 TI - Nonlocal Diffusion and Applications AU - Bucur, Claudia AU - Valdinoci, Enrico PY - 2016 SN - 9783319287393 PB - Cham Springer International Publishing DB - UniCat KW - Algebra KW - Functional analysis KW - Partial differential equations KW - Mathematical analysis KW - Numerical methods of optimisation KW - Mathematics KW - differentiaalvergelijkingen KW - algebra KW - analyse (wiskunde) KW - functies (wiskunde) KW - wiskunde KW - kansrekening KW - optimalisatie UR - https://www.unicat.be/uniCat?func=search&query=sysid:131563281 AB - 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. ER -