Timeline for Symmetry Properties of Minimizers - Calculus of Variations
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| Oct 10, 2013 at 22:27 | comment | added | Otis Chodosh | Nice answer! Something similar to your "rearrangement argument" section is the fact that first eigenfunctions of say, the Dirichlet problem in a domain of $\mathbb{R}^2$ inherit the same symmetries of the domain: because the first eigenspace is one dim'l and spanned by a positive function, it's clear that the "flip" of the eigenfunction must be equal to itself. | |
| Oct 8, 2013 at 5:51 | history | answered | Kelei Wang | CC BY-SA 3.0 |