Finding critical points whose polarization is also a critical point
Keywords
Symmetry of solutions of semi-linear elliptic PDEs, mountain pass lemma, general minimax principle, symmetrization, polarization, non-smooth critical point theoryAbstract
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.Downloads
Published
2012-04-23
How to Cite
1.
SQUASSINA, Marco and VAN SCHAFTINGEN, Jean. Finding critical points whose polarization is also a critical point. Topological Methods in Nonlinear Analysis. Online. 23 April 2012. Vol. 40, no. 2, pp. 371 - 379. [Accessed 19 April 2024].
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