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In: Mathematische Schriften Kassel 18, 01 / (2018-01-23) , S. ;
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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.
@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} }