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arXiv · 1108.6217

Finding critical points whose polarization is also a critical point

Marco Squassina·Jean Van Schaftingen
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Abstract

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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Marco Squassina, Jean Van Schaftingen. 2011-11-28. Finding critical points whose polarization is also a critical point. https://arxiv.org/abs/1108.6217

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