Finding critical points whose polarization is also a critical point
(2012) Topological Methods in Nonlinear Analysis — Vol. 40, n° 2, p. 371-379 (2012)
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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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Citations
Van Schaftingen, J., & Van Schaftingen, J. (2012). Finding critical points whose polarization is also a critical point. Topological Methods in Nonlinear Analysis, 40(2), 371-379. https://hdl.handle.net/2078.5/246347 (Original work published 2012)