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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Gradient higher integrability for double phase problems on metric measure spaces
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by Juha Kinnunen, Antonella Nastasi and Cintia Pacchiano Camacho
Proc. Amer. Math. Soc. 152 (2024), 1233-1251
DOI: https://doi.org/10.1090/proc/16646
Published electronically: January 18, 2024

Abstract:

We study local and global higher integrability properties for quasiminimizers of a class of double phase integrals characterized by nonstandard growth conditions. We work purely on a variational level in the setting of a metric measure space with a doubling measure and a Poincaré inequality. The main novelty is an intrinsic approach to double phase Sobolev-Poincaré inequalities.
References
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Bibliographic Information
  • Juha Kinnunen
  • Affiliation: Department of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
  • MR Author ID: 349676
  • Email: juha.k.kinnunen@aalto.fi
  • Antonella Nastasi
  • Affiliation: Department of Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy
  • MR Author ID: 1118991
  • ORCID: 0000-0003-1589-2235
  • Email: antonella.nastasi@unipa.it
  • Cintia Pacchiano Camacho
  • Affiliation: Department of Mathematics and Statistics, University of Calgary, 2500 University Dr. NW, Calgary, Alberta T2X 3B5, Canada
  • MR Author ID: 1460219
  • Email: cintia.pacchiano@ucalgary.ca
  • Received by editor(s): May 18, 2023
  • Received by editor(s) in revised form: August 7, 2023, and August 9, 2023
  • Published electronically: January 18, 2024
  • Additional Notes: Part of this material was based upon work supported by the Swedish Research Council while the first author and the second author were in residence at Institut Mittag-Leffler in Djursholm, Sweden during the Research Program Geometric Aspects of Nonlinear Partial Differential Equations in 2022. The second author was partly supported by GNAMPA-INdAM Project 2022 “Equazioni differenziali alle derivate parziali in fenomeni non lineari” and by GNAMPA-INdAM Project 2023 “Regolarità per problemi ellittici e parabolici con crescite non standard”. The third author was supported by a doctoral training grant for 2022 and a travel grant from the Väisälä Fund
    The second author is a member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM)
  • Communicated by: Nageswari Shanmugalingam
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 1233-1251
  • MSC (2020): Primary 49Q20, 49N60, 31C45, 35J60, 46E35
  • DOI: https://doi.org/10.1090/proc/16646
  • MathSciNet review: 4693679