On the Second Inner Variation of the Allen-Cahn Functional and Its Applications
نویسنده
چکیده
In this paper, we study the relation between the second inner variations of the Allen-Cahn functional and its Gamma-limit, the area functional. Our result implies that the Allen-Cahn functional only approximates well the area functional up to the first order. However, as an application of our result, we prove, assuming the singlemultiplicity property of the limiting energy, that the Morse indices of critical points of the Allen-Cahn functional are bounded from below by the Morse index of the limiting minimal hypersurface.
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Article history: Received 18 September 2014 Available online 4 November 2014 MSC: 49A50 49J45 58E12
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