Finding critical points whose polarization is also a critical point
Słowa kluczowe
Symmetry of solutions of semi-linear elliptic PDEs, mountain pass lemma, general minimax principle, symmetrization, polarization, non-smooth critical point theoryAbstrakt
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.Pobrania
Opublikowane
2012-04-23
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1.
SQUASSINA, Marco & VAN SCHAFTINGEN, Jean. Finding critical points whose polarization is also a critical point. Topological Methods in Nonlinear Analysis [online]. 23 kwiecień 2012, T. 40, nr 2, s. 371–379. [udostępniono 18.9.2024].
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