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Datum
2018-01-23Autor
Stylianou, AthanasiosSchlagwort
510 MathematikMetadata
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On the existence of symmetric minimizers
Zusammenfassung
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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@article{urn:nbn:de:hebis:34-2018012354238,
author={Stylianou, Athanasios},
title={On the existence of symmetric minimizers},
year={2018}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2018$n2018 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2018012354238 3000 Stylianou, Athanasios 4000 On the existence of symmetric minimizers / Stylianou, Athanasios 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2018012354238=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 18, 01 7136 ##0##urn:nbn:de:hebis:34-2018012354238
2018-01-23T14:16:52Z 2018-01-23T14:16:52Z 2018-01-23 urn:nbn:de:hebis:34-2018012354238 http://hdl.handle.net/123456789/2018012354238 eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Inheritance of symmetry Haar measure G-average 510 On the existence of symmetric minimizers Preprint 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. open access Stylianou, Athanasios Mathematische Schriften Kassel ;; 18, 01 35B06 58D19 46G10 Mathematische Schriften Kassel 18, 01
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