An evolutionary Haar-Rado type theorem
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
Published inManuscripta Mathematica
© The Author(s) 2021
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.
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