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

For a solution of the Allen–Cahn equation in R 2 , 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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Veröffentlicht in:	Nonlinear differential equations and applications 2017, Vol.24 (5)
1. Verfasser:	Wang, Kelei
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Blowing Mathematics Mathematics and Statistics
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container_title	Nonlinear differential equations and applications
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description	For a solution of the Allen–Cahn equation in R 2 , 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.
doi_str_mv	10.1007/s00030-017-0481-7
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subjects	Analysis Blowing Mathematics Mathematics and Statistics
title	Some remarks on the structure of finite Morse index solutions to the Allen–Cahn equation in R2
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