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Uniqueness and comparison principle for Trudinger's parabolic equation with Hölder continuous boundary values
Abstract
For every p > 1, we establish uniqueness and comparison principle for Trudinger's parabolic equation ∂t (|u|p−2u) = div(|∇ u|p−2∇ u) in Ω× (0,T), assuming suitable Hölder regularity for the boundary values. Our comparison principle applies to sign-changing weak sub- and supersolutions. As an application, we obtain uniqueness of weak solutions to Cauchy--Dirichlet problems when the lateral boundary data is suitably Hölder continuous in time. In particular, Lipschitz continuous boundary values are covered.
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BibTeX
@misc{anttila2026uniqueness,
title = {{Uniqueness and comparison principle for Trudinger's parabolic equation with Hölder continuous boundary values}},
author = {Riku Anttila and Mikko Parviainen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37835},
eprint = {2610.37835},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37835},
}
RIS
TY - UNPB
TI - Uniqueness and comparison principle for Trudinger's parabolic equation with Hölder continuous boundary values
AU - Riku Anttila
AU - Mikko Parviainen
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37835
UR - https://arxiv.org/abs/2610.37835
AB - For every p > 1, we establish uniqueness and comparison principle for Trudinger's parabolic equation ∂_t (|u|^p−2u) = div(|∇ u|^p−2∇ u) in Ω× (0,T), assuming suitable Hölder regularity for the boundary values. Our comparison principle applies to sign-changing weak sub- and supersolutions. As an application, we obtain uniqueness of weak solutions to Cauchy--Dirichlet problems when the lateral boundary data is suitably Hölder continuous in time. In particular, Lipschitz continuous boundary values are covered.
ER -