Preprint Article Version 17 Preserved in Portico This version is not peer-reviewed

Duality Principles and Numerical Procedures for a Large Class of Non-convex Models in the Calculus of Variations

Fabio Botelho
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How to cite: Botelho, F. Duality Principles and Numerical Procedures for a Large Class of Non-convex Models in the Calculus of Variations. Preprints 2023, 2023020051. https://doi.org/10.20944/preprints202302.0051.v17 Botelho, F. Duality Principles and Numerical Procedures for a Large Class of Non-convex Models in the Calculus of Variations. Preprints 2023, 2023020051. https://doi.org/10.20944/preprints202302.0051.v17

Abstract

This article develops duality principles and numerical results for a large class of non-convex variational models. The main results are based on fundamental tools of convex analysis, duality theory and calculus of variations. More specifically the approach is established for a class of non-convex functionals similar as those found in some models in phase transition. Finally, in the last section we present a concerning numerical example and the respective software.

Keywords

Duality theory; non-convex analysis; numerical method for a non-smooth model

Subject

Computer Science and Mathematics, Applied Mathematics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1
Received: 19 June 2023
Commenter: Fabio Botelho
Commenter's Conflict of Interests: Author
Comment: We have revised all the duality principles.

We have removed those duality principles which  their proofs were not perfect yet.

For such results, more developments are necessary, which we postpone for a future research.

Finally, we have included a new section on the Galerkin functional and new numerical examples concerning the Legendre-Galerkin formulation.
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