On the second inner variation of the Allen-Cahn Functional and its applications
Analysis of PDEs
2010-09-29 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1009.5649,
title = {On the second inner variation of the Allen-Cahn Functional and its applications},
author = {Nam Q. Le},
journal= {arXiv preprint arXiv:1009.5649},
year = {2010}
}
Comments
to appear in Indiana Univ. Math. J