Europe/Lisbon —

Kelei Wang

Kelei Wang, Wuhan University

In this talk I will survey the regularity theory for transition layers in singularly perturbed Allen-Cahn equation, from zeroth order regularity to second order one. Some applications of this regularity theory will also be discussed, including De Giorgi conjecture, classification of finite Morse index solutions and construction of minimal hypersurfaces by Allen-Cahn approximation.