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Higher regularity of uniform local minimizers in Calculus of Variations


Authors: Worku T. Bitew and Yury Grabovsky
Journal: Proc. Amer. Math. Soc. 145 (2017), 5215-5222
MSC (2010): Primary 49-02
DOI: https://doi.org/10.1090/proc/13639
Published electronically: June 22, 2017
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Abstract: This paper presents a simple proof of $ W^{2,2}_{\rm loc}$ regularity of Lipschitz uniform local minimizers of vectorial variational problems. The method is based on the idea that inner variations provide constraints on the structure of singularities of local minimizers.


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Additional Information

Worku T. Bitew
Affiliation: Department of Mathematics, Farmingdale State College, SUNY, Farmingdale, New York 11735
Email: biteww@farmingdale.edu

Yury Grabovsky
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email: yury@temple.edu

DOI: https://doi.org/10.1090/proc/13639
Received by editor(s): July 16, 2008
Received by editor(s) in revised form: December 26, 2016
Published electronically: June 22, 2017
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society

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