A1 Journal article (refereed)
An evolutionary Haar-Rado type theorem (2022)

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

JYU authors or editors

Publication details

All authors or editors: Rainer, Rudolf; Siltakoski, Jarkko; Stanin, Thomas

Journal or series: Manuscripta Mathematica

ISSN: 0025-2611

eISSN: 1432-1785

Publication year: 2022

Publication date: 03/04/2021

Volume: 168

Issue number: 1-2

Pages range: 65-88

Publisher: Springer

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s00229-021-01293-8

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/75004

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.

Keywords: partial differential equations; calculus of variations

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2022

Preliminary JUFO rating: 1