Finding critical points whose polarization is also a critical point

Details Finding critical points whose polarization is also a critical point Finding critical points whose polarization is also a critical point

2011-08-31

arxiv.org/abs/1108.6217v2

Mathematics

Analysis of PDEs

7 pages

Scientific paper

We show that near any given minimizing sequence of paths for the mountain pass lemma, there exists a critical point whose polarization is also a critical point. This is motivated by the fact that if any polarization of a critical point is also a critical point and the Euler-Lagrange equation is a second-order semi-linear elliptic problem, T. Bartsch, T. Weth and M. Willem (J. Anal. Math., 2005) have proved that the critical point is axially symmetric.

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