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On the existence of symmetric minimizers

In this note we revisit a less known symmetrization method for functions with respect to a topological group, which we call G-averaging. We note that, although quite non-technical in nature, this method yields G-invariant minimizers of functionals satisfying some relaxed convexity properties. We give an abstract theorem and show how it can be applied to the p-Laplace and polyharmonic Poisson problem in order to construct symmetric solutions. We also pose some open problems and explore further possibilities where the method of G-averaging could be applied to.

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In: Mathematische Schriften Kassel 18, 01 / (2018-01-23) , S. ;
@article{urn:nbn:de:hebis:34-2018012354238,
  author    ={Stylianou, Athanasios},
  title    ={On the existence of symmetric minimizers},
  copyright  ={https://rightsstatements.org/page/InC/1.0/},
  language ={en},
  year   ={2018-01-23}
}