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Journal of Convex Analysis 25 (2018), No. 2, 675--690
Copyright Heldermann Verlag 2018

New Challenges on the Regularity of Minimizers of Functionals

Maria Alessandra Ragusa
Dip. di Matematica e Informatica, UniversitÓ di Catania, Viale A. Doria 6, 95125 Catania, Italy

Atsushi Tachikawa
Dept. of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan

Our aim is to obtain regularity of minimizers of functionals under the nonstandard growth conditions. Starting point is the study made by the authors finalized to investigate the regularity of the minimizers of quadratic functionals, whose integrands have vanishing mean oscillation coefficients, using some majorizations for the functionals, rather than the well known Euler's equation associated with it.

Keywords: Regularity, minimizers, non-stardard growth.

MSC: 49N60,35J50; 58E20

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