Hölder continuity and Harnack estimate for non-homogeneous parabolic equations
Abstract
In this paper we continue the study on intrinsic Harnack inequality for non-homogeneous parabolic equations in non-divergence form initiated by the first author in Arya (Calc Var Partial Differ Equ 61:30–31, 2022). We establish a forward-in-time intrinsic Harnack inequality, which in particular implies the Hölder continuity of the solutions. We also provide a Harnack type estimate on global scale which quantifies the strong minimum principle. In the time-independent setting, this together with Arya (2022) provides an alternative proof of the generalized Harnack inequality proven by the second author in Julin (Arch Ration Mech Anal 216:673–702, 2015).
Main Authors
Format
Articles
Research article
Published
2024
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202409095857Use this for linking
Review status
Peer reviewed
ISSN
0025-5831
DOI
https://doi.org/10.1007/s00208-024-02979-6
Language
English
Published in
Mathematische Annalen
Citation
- Arya, V., & Julin, V. (2024). Hölder continuity and Harnack estimate for non-homogeneous parabolic equations. Mathematische Annalen, Early online. https://doi.org/10.1007/s00208-024-02979-6
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Funder(s)
Research Council of Finland
Funding program(s)
Research costs of Academy Research Fellow, AoF
Akatemiatutkijan tutkimuskulut, SA
Additional information about funding
The authors were supported by the Academy of Finland grant 314227.
Open Access funding provided by University of Jyväskylä (JYU).
Copyright© The Author(s) 2024