A note on the Morse index of 2k-ended phase transitions in R^2

Abstract

We show that the Morse index of every 2k-ended solution of the Allen-Cahn equation in R^2 is >= k-1. This bound is expected to be sharp.

This paper has been superseded by arXiv:1706.05946. Minor misprints corrected

References in corpus (1)

• Finite Morse index implies finite ends

Cited by in corpus (1)

• A complete classification of finite Morse index solutions to elliptic sine-Gordon equation in the plane