Year: 2026
Type: preprint
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 $L^\infty$ 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.
Source: arXiv (Cornell University)
Authors: Hao, Xia, Li, Yan, Zhao, Zhiwen
Institution: Hebei Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213530365