Finding critical points whose polarization is also a critical point
KeywordsSymmetry of solutions of semi-linear elliptic PDEs, mountain pass lemma, general minimax principle, symmetrization, polarization, non-smooth critical point theory
AbstractWe 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.
How to Cite
SQUASSINA, Marco & VAN SCHAFTINGEN, Jean. Finding critical points whose polarization is also a critical point. Topological Methods in Nonlinear Analysis [online]. 23 April 2012, T. 40, nr 2, s. 371–379. [accessed 7.2.2023].
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