Some remarks on the structure of finite Morse index solutions to the Allen-Cahn equation in ℝ²

2015/06/01 by Kelei Wang, Wang, Kelei
Mathematics · #35B08 #35B35 #35J61 #35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B08 #msc:35B35 #msc:35J61 #msc:35R35

paper · pdf · doi:10.48550/arxiv.1506.00499

13 pages

arxiv created 2015/10/29 · arxiv updated 2015/10/30

Abstract

For a solution of the Allen-Cahn equation in ℝ², under the natural linear growth energy bound, we show that the blowing down limit is unique. Furthermore, if the solution has finite Morse index, the blowing down limit satisfies the multiplicity one property.

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