Abstract
We establish the Lipschitz regularity of the a priori bounded local minimizers of integral functionals with non autonomous energy densities satisfying non standard growth conditions under a bound on the gap between the growth and the ellipticity exponent that is reminiscent of the sharp bound already found in [16].
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Acknowledgements
M. Eleuteri and A. Passarelli di Napoli have been partially supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) also through the INdAM-GNAMPA projects CUP_E53C23001670001 and CUP_E53C22001930001. Moreover M. Eleuteri has been partially supported by PRIN 2020 “Mathematics for industry 4.0 (Math4I4)” (coordinator P. Ciarletta) while A. Passarelli di Napoli has been partially supported by Università degli Studi di Napoli Federico II through the Project FRA ( 000022-75-2021-FRA-PASSARELLI) and by the Sustainable Mobility Center (Centro Nazionale per la Mobilità Sostenibile - CNMS) Spoke 10 Logistica Merci. The authors wish to thank Prof. F. Leonetti for useful suggestions and comments.
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Eleuteri, M., Passarelli di Napoli, A. Lipschitz Regularity for a Priori Bounded Minimizers of Integral Functionals with Nonstandard Growth. Potential Anal (2024). https://doi.org/10.1007/s11118-024-10146-4
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DOI: https://doi.org/10.1007/s11118-024-10146-4