Group invariant variational principles

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 inv...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Falcó, Javier, Isert, Daniel
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Convexity
Invariants
Theorems
Variational principles
Online Access:Get full text
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Summary: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 Brønsted-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.
ISSN:2331-8422