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 in
Manuscripta MathematicaDate
2022Copyright
© 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.
Publisher
SpringerISSN Search the Publication Forum
0025-2611Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/66333684
Metadata
Show full item recordCollections
Additional information about funding
Open access funding provided by Paris Lodron University of Salzburg.License
Related items
Showing items with similar title or keywords.
-
The rank-one theorem on RCD spaces
Antonelli, Gioacchino; Brena, Camillo; Pasqualetto, Enrico (Mathematical Sciences Publishers, 2024)We extend Alberti’s rank-one theorem to RCD(K, N) metric measure spaces -
Optimization of the domain in elliptic variational inequalities
Neittaanmäki, Pekka; Sokolowski, J.; Zolesio, J. P. (University of Jyväskylä, 1986) -
A two-phase problem with Robin conditions on the free boundary
Guarino Lo Bianco, Serena; La Manna, Domenico Angelo; Velichkov, Bozhidar (Les Éditions de l'École polytechnique, 2021)We study for the first time a two-phase free boundary problem in which the solution satisfies a Robin boundary condition. We consider the case in which the solution is continuous across the free boundary and we prove an ... -
Stationary sets of the mean curvature flow with a forcing term
Julin, Vesa; Niinikoski, Joonas (Walter de Gruyter GmbH, 2023)We consider the flat flow solution to the mean curvature equation with forcing in ℝn. Our main resultstates that tangential balls in ℝn under a flat flow with a bounded forcing term will experience fattening, which generalizes ... -
The bounded slope condition for parabolic equations with time-dependent integrands
Schätzler, Leah; Siltakoski, Jarkko (Birkhäuser, 2023)