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arXiv · 2306.06484

Group invariant variational principles

Javier Falcó·Daniel Isert
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Abstract

In this paper we introduce a group invariant version of the wellknown Ekeland variational principle. To achieve this, we defne the concept of convexity with respect to a group and establish a version of the theorem within this framework. Additionally, we present several consequences of the group invariant Ekeland variational principle, including Palais-Smale minimizing sequences, the Br{\o}nsted-Rockafellar theorem, and a characterization of the linear and continuous group invariant functionals space. Moreover, we provide an alternative proof of the Bishop-Phelps theorem and proofs for the group-invariant Hahn-Banach separating theorems. Finally, we discuss some implications and applications of these results.

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Javier Falcó, Daniel Isert. 2023-06-10. Group invariant variational principles. https://arxiv.org/abs/2306.06484

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