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 th...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.展开更多
基金partially supported by Natural Sciences and Engineering Research Council of Canada
文摘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.
