The fractional Laplacian is a nonlocal operator naturally arising in several branches of pure and applied mathematics. It presents intriguing features and possesses a great flexibility to a number of applications in physics, biology, numerics and finance.
After briefly discussing the basics of this operator and some concrete applications, we will consider in some detail the case of nonlocal minimal surfaces.
In particular, the regularity of these objects seems to be a rather challenging topic. Nonlocal minimal surfaces also exhibit stickiness phenomena that are special for the nonlocal setting and have no classical counterpart.
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