On the Hölder regularity of signed solutions to a doubly nonlinear equation
Bögelein V, Duzaar F, Liao N (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 281
Article Number: 109173
Journal Issue: 9
DOI: 10.1016/j.jfa.2021.109173
Abstract
We establish the interior and boundary Hölder continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is ∂t(|u|p−2u)−Δpu=0,p>1. The proof relies on the property of expansion of positivity and the method of intrinsic scaling, all of which are realized by De Giorgi's iteration. Our approach, while emphasizing the distinct roles of sub(super)-solutions, is flexible enough to obtain the Hölder regularity of solutions to initial-boundary value problems of Dirichlet type or Neumann type in a cylindrical domain, up to the parabolic boundary. In addition, based on the expansion of positivity, we are able to give an alternative proof of Harnack's inequality for non-negative solutions. Moreover, as a consequence of the interior estimates, we also obtain a Liouville-type result.
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APA:
Bögelein, V., Duzaar, F., & Liao, N. (2021). On the Hölder regularity of signed solutions to a doubly nonlinear equation. Journal of Functional Analysis, 281(9). https://dx.doi.org/10.1016/j.jfa.2021.109173
MLA:
Bögelein, Verena, Frank Duzaar, and Naian Liao. "On the Hölder regularity of signed solutions to a doubly nonlinear equation." Journal of Functional Analysis 281.9 (2021).
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