Note on time-regularity for weak solutions to parabolic systems of $p$-Laplace type
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- by Simon Bortz, Moritz Egert and Olli Saari PDF
- Proc. Amer. Math. Soc. 149 (2021), 1677-1685 Request permission
Abstract:
We show that local weak solutions to parabolic systems of $p$-Laplace type are Hölder continuous in time with values in a spatial Lebesgue space and Hölder continuous on almost every time line. We provide an elementary and self-contained proof building on the local higher integrability result of Kinnunen and Lewis.References
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Additional Information
- Simon Bortz
- Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama, 35487
- MR Author ID: 1166754
- ORCID: 0000-0001-7955-3035
- Email: sbortz@ua.edu
- Moritz Egert
- Affiliation: CNRS, Laboratoire de mathématiques d’Orsay, Université Paris-Saclay, 91405, Orsay, France
- MR Author ID: 1042848
- ORCID: 0000-0003-3638-3448
- Email: moritz.egert@universite-paris-saclay.fr
- Olli Saari
- Affiliation: Mathematical Institute, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany
- MR Author ID: 1139147
- ORCID: 0000-0003-1212-8100
- Email: saari@math.uni-bonn.de
- Received by editor(s): December 13, 2019
- Received by editor(s) in revised form: September 10, 2020
- Published electronically: February 11, 2021
- Additional Notes: This research was supported by the CNRS through a PEPS JCJC project and by DFG through DFG SFB 1060 and DFG EXC 2047
- Communicated by: Ryan Hynd
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 1677-1685
- MSC (2020): Primary 35K55, 42B15
- DOI: https://doi.org/10.1090/proc/15344
- MathSciNet review: 4242322