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February 2022 Hölder continuity for vectorial local minimizers of variational integrals
Yanan Shan, Hongya Gao
Rocky Mountain J. Math. 52(1): 289-297 (February 2022). DOI: 10.1216/rmj.2022.52.289

Abstract

This note deals with vectorial local minimizers of some integral functionals related to nonlinear elasticity theory. Under some structural assumptions, we derive that each component of the local minimizers lies in the De Giorgi class, thus the minimizers are locally Hölder continuous. We emphasize that no convexity is assumed. On the other hand, a special dependence on minors, taken from the Jacobian matrix, plays an important role in the proof.

Citation

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Yanan Shan. Hongya Gao. "Hölder continuity for vectorial local minimizers of variational integrals." Rocky Mountain J. Math. 52 (1) 289 - 297, February 2022. https://doi.org/10.1216/rmj.2022.52.289

Information

Received: 24 May 2021; Revised: 2 July 2021; Accepted: 4 July 2021; Published: February 2022
First available in Project Euclid: 19 April 2022

Digital Object Identifier: 10.1216/rmj.2022.52.289

Subjects:
Primary: 49N60

Keywords: De Giorgi class , Hölder continuity , Integral functionals , vectorial local minimizer

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 1 • February 2022
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