Higher regularity of uniform local minimizers in Calculus of Variations
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Abstract:
This paper presents a simple proof of $W^{2,2}_\textrm {loc}$ 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.References
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Additional Information
- Worku T. Bitew
- Affiliation: Department of Mathematics, Farmingdale State College, SUNY, Farmingdale, New York 11735
- MR Author ID: 893329
- Email: biteww@farmingdale.edu
- Yury Grabovsky
- Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
- MR Author ID: 338656
- Email: yury@temple.edu
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5215-5222
- MSC (2010): Primary 49-02
- DOI: https://doi.org/10.1090/proc/13639
- MathSciNet review: 3717950