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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Nam Le
Indiana University
Title: Second inner variations of Allen-Cahn type energies and applications to local minimizers

Abstract: We will discuss the mysterious discrepancy between the limit of the second inner variations of p-Laplace Allen-Cahn energies and that of their Gamma-limit which is the area functional. This discrepancy is a condimension one phenomenon and is related to the convergence of certain 4-tensors. Two applications of our analysis will be discussed. First, we partially answer a question of Kohn and Sternberg by giving a relation between the limit of second variations of the Allen-Cahn functional and the second inner variation of the area functional at local minimizers. Second, we reveal an interesting identity connecting second inner variation and Poincare inequality for area-minimizing surfaces with volume constraint in the work of Sternberg and Zumbrun.

Recording: http://mm.math.cmu.edu/recordings/cna/CNA-NamLe-Apr-14-2015.avi
Recording: http://mm.math.cmu.edu/recordings/cna/CNA-NamLe-Apr-14-2015.mp4
Date: Tuesday, April 14, 2015
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  David Kinderlehrer