Mathematics – Analysis of PDEs
Scientific paper
2010-09-28
Mathematics
Analysis of PDEs
to appear in Indiana Univ. Math. J
Scientific paper
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.
Le Nam Q.
No associations
LandOfFree
On the second inner variation of the Allen-Cahn Functional and its applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the second inner variation of the Allen-Cahn Functional and its applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the second inner variation of the Allen-Cahn Functional and its applications will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-694809