Journal
INDIANA UNIVERSITY MATHEMATICS JOURNAL
Volume 60, Issue 6, Pages 1843-1856Publisher
INDIANA UNIV MATH JOURNAL
DOI: 10.1512/iumj.2011.60.4505
Keywords
Allen-Cahn functional; second variation; Morse index; stability
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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 single-multiplicity 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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