摘要
In 1979,De Giorgi conjectured that the only bounded monotone solutions to the Allen-Cahn equation △u+u-u^3=0 in R^N,are one-dimensional.This conjecture and its connection with minimal surfaces and Toda systems are the subject of this survey article.
In 1979,De Giorgi conjectured that the only bounded monotone solutions to the Allen-Cahn equation △u＋u-u-3=0 in R-N,are one-dimensional.This conjecture and its connection with minimal surfaces and Toda systems are the subject of this survey article.
基金
partially supported by Natural Sciences and Engineering Research Council of Canada
