An evolutionary Haar-Rado type theorem
Abstract
In this paper, we study variational solutions to parabolic equations of the type ∂t u −divx (Dξ f (Du))+ Du g(x, u) = 0, where u attains time-independent boundary values u0 on the parabolic boundary and f, g fulfill convexity assumptions. We establish a Haar-Rado type theorem: If the boundary values u0 admit a modulus of continuity ω and the estimate |u(x, t)−u0(γ )| ≤ ω(|x −γ |) holds, then u admits the same modulus of continuity in the spatial variable.
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202104092316Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0025-2611
DOI
https://doi.org/10.1007/s00229-021-01293-8
Language
English
Published in
Manuscripta Mathematica
Citation
- Rainer, R., Siltakoski, J., & Stanin, T. (2022). An evolutionary Haar-Rado type theorem. Manuscripta Mathematica, 168(1-2), 65-88. https://doi.org/10.1007/s00229-021-01293-8
License
Additional information about funding
Open access funding provided by Paris Lodron University of Salzburg.
Copyright© The Author(s) 2021