Symmetrization and minimax principles
(2005) Communications in Contemporary Mathematics — Vol. 7, n° 4, p. 463-481 (2005)
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- Abstract
- We develop a method to prove that some critical levels for functionals invariant by symmetry obtained by minimax methods without any symmetry constraint are attained by symmetric critical points. It is used to investigate the symmetry properties of solutions of elliptic partial differential equations with Dirichlet or Neumann boundary conditions. It is also an alternative to concentration-compactness for some symmetric elliptic problems.
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Van Schaftingen, J. (2005). Symmetrization and minimax principles. Communications in Contemporary Mathematics, 7(4), 463-481. https://doi.org/10.1142/S0219199705001817 (Original work published 2005)