2021/04/08 by Grafke, Tobias, Scholtes, Sebastian, Wagner, Alfred +1
#35B38 #49J40 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2104.03689
We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in d≥ 2 and the critical parameter regime of large system size and mean value close to -1. We employ the String Method of E, Ren, and Vanden-Eijnden -- a numerical algorithm for computing transition pathways in complex systems -- in d=2 to gain additional insight into the properties of the minima and saddle point. Motivated by the numerical observations, we adapt a method of Caffarelli and Spruck to study convexity of level sets in d≥ 2.