On the Local boundedness and higher integrability for the subcritical doubly nonlinear parabolic systems
Year: 2026
Type: preprint
Abstract: We consider the inhomogeneous doubly nonlinear parabolic systems of the form \begin{equation*}\partial_t (|u|^{q-1}u)-\operatorname{div}(|Du|^{p-2}Du)=\operatorname{div}(|F|^{p-2}F)\end{equation*} in a bounded space-time cylinder $Ω_T=Ω\times(0,T)\subset \mathbb{R}^{N+1}$. We study the local regularity properties for weak solutions in the subcritical range $p\leq\frac{N(q+1)}{N+q+1}$ and $00$. In addition, we prove local higher integrability of $|Du|$ in the range $p=\frac{N(q+1)}{N+q+1}$ and $\frac{N+p}{N-p}
Source: arXiv (Cornell University)
Author: Li, Qifan
Institution: Wuhan University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203862394