Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions: Cetraro, Italy 2016

Description

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. Front Matter ....Pages i-ix The Geometry of Diffusing and Self-Attracting Particles in a One-Dimensional Fair-Competition Regime (Vincent Calvez, José Antonio Carrillo, Franca Hoffmann)....Pages 1-71 Bubbling Blow-Up in Critical Parabolic Problems (Manuel del Pino)....Pages 73-116 Regularity Theory for Local and Nonlocal Minimal Surfaces: An Overview (Matteo Cozzi, Alessio Figalli)....Pages 117-158 Short Tales from Nonlinear Calderón-Zygmund Theory (Giuseppe Mingione)....Pages 159-204 The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (Juan Luis Vázquez)....Pages 205-278 Back Matter ....Pages 279-280