A duality principle and an existence result for a non-linear model in elasticity and relaxation for related models in phase transition

Fabio Silva  Botelho

doi:10.59400/jam2386

A duality principle and an existence result for a non-linear model in elasticity and relaxation for related models in phase transition

Fabio Silva Botelho Department of Mathematics, Federal University of Santa Catarina (UFSC), Florianópolis 88040 900, Brazil

Article ID: 2386

DOI: https://doi.org/10.59400/jam2386

Keywords: duality principle; non-linear model in elasticity; global existence result

Abstract

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual variational formulation for a non-linear model in elasticity. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual formulation obtained may be applied to a large class of similar models in the calculus of variations. In a subsequent section, we present a global existence result for such a concerning model in elasticity. Finally, in the last sections, we develop duality principles and relaxation procedures for a related model in phase transition.

Published

2025-05-12

How to Cite

Botelho, F. S. (2025). A duality principle and an existence result for a non-linear model in elasticity and relaxation for related models in phase transition. Journal of AppliedMath, 3(3), 2386. https://doi.org/10.59400/jam2386

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Vol. 3 No. 3 (2025)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

References

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[21]Botelho FS. A Duality Principle and an Existence Result for a Non-linear Model in Elasticity and Relaxation for Related Models in Phase Transition. Technical Research Repository. 2024; in press.

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International Islamic University, Pakistan

Dr. Nehad Ali Shah

Sejong University, Korea

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