PreprintarXiv licencearXiv
Local behavior of solutions to inhomogeneous singular parabolic p-Laplace equations
Abstract
It is known that a major difficulty in proving Hölder regularity for solutions to quasilinear singular parabolic equations of p-Laplace type via the method of intrinsic scaling is to establish the decay estimate of the space-time measure of level sets. In this paper, we consider an inhomogeneous singular parabolic p-Laplace equation with nonnegative time-independent forcing and Dirichlet data. By combining a time-rescaling argument with L∞ comparison estimates, we derive Lipschitz regularity in time after any fixed positive elapsed time, which reduces the problem to an elliptic-type decay estimate for the spatial measure of level sets that is essentially uniform in time. This reduction enables us to address the above obstacle.
Related
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BibTeX
@misc{hao2026local,
title = {{Local behavior of solutions to inhomogeneous singular parabolic $p$-Laplace equations}},
author = {Xia Hao and Yan Li and Zhiwen Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18815},
eprint = {2609.18815},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18815},
}
RIS
TY - UNPB
TI - Local behavior of solutions to inhomogeneous singular parabolic p-Laplace equations
AU - Xia Hao
AU - Yan Li
AU - Zhiwen Zhao
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.18815
UR - https://arxiv.org/abs/2609.18815
AB - It is known that a major difficulty in proving Hölder regularity for solutions to quasilinear singular parabolic equations of p-Laplace type via the method of intrinsic scaling is to establish the decay estimate of the space-time measure of level sets. In this paper, we consider an inhomogeneous singular parabolic p-Laplace equation with nonnegative time-independent forcing and Dirichlet data. By combining a time-rescaling argument with L^∞ comparison estimates, we derive Lipschitz regularity in time after any fixed positive elapsed time, which reduces the problem to an elliptic-type decay estimate for the spatial measure of level sets that is essentially uniform in time. This reduction enables us to address the above obstacle.
ER -