Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions

Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems. The authors are some of the most well-known mathematicians in this innovative field, which is presently undergoing rapid development. The intended audience includes experts in elliptic and parabolic equations who are interested in extending their expertise to the nonlinear setting, as well as Ph.D. or postdoctoral students who want to enter into the most promising research topics in the field.

Clearly presented, with a particular emphasis on introducing young students to important research topics Features a state-of-the-art description of rapidly developing topics in nonlinear, nonlocal diffusions and interactions Authored by well-known researchers, who have the capacity to single out some of the most promising topics in stationary and evolutionary local and nonlocal PDEs Includes supplementary material: sn.pub/extras

Inhalt
Vincent Calvez, José Antonio Carrillo, and Franca Hoffmann The geometry of diffusing and self-attracting particles in a one-dimensional fair-competition regime.- Manuel del Pino: Bubbling blow-up in critical parabolic problems.- Matteo Cozzi and Alessio Figalli: Regularity theory for local and nonlocal minimal surfaces: an overview.- Giuseppe Mingione: Short Tales from Nonlinear Calderón-Zygmund Theory.- Juan Luis Vazquez: The mathematical theories of diffusion: Nonlinear and fractional diffusion.