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On the Local boundedness and higher integrability for the subcritical doubly nonlinear parabolic systems
Abstract
We consider the inhomogeneous doubly nonlinear parabolic systems of the form ∂t (|u|q−1u)−div(|Du|p−2Du)=div(|F|p−2F) in a bounded space-time cylinder ΩT=Ω×(0,T)⊂ ℝN+1. We study the local regularity properties for weak solutions in the subcritical range p≤(N(q+1))/(N+q+1) and 0<q<(N+2)/(N−2). Under an extra integrability assumption |u|∈ Llocrr(ΩT), we establish a quantitative bound for |u|. Here, the exponent rr satisfies λrr=N(p−q−1)+prr>0. In addition, we prove local higher integrability of |Du| in the range p=(N(q+1))/(N+q+1) and (N+p)/(N−p)<q<(N+2)/(N−2), provided that |u|∈ Llocrr(ΩT) holds.
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BibTeX
@misc{li2026local,
title = {{On the Local boundedness and higher integrability for the subcritical doubly nonlinear parabolic systems}},
author = {Qifan Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.19909},
eprint = {2608.19909},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.19909},
}
RIS
TY - UNPB
TI - On the Local boundedness and higher integrability for the subcritical doubly nonlinear parabolic systems
AU - Qifan Li
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2608.19909
UR - https://arxiv.org/abs/2608.19909
AB - We consider the inhomogeneous doubly nonlinear parabolic systems of the form ∂_t (|u|^q−1u)−div(|Du|^p−2Du)=div(|F|^p−2F) in a bounded space-time cylinder Ω_T=Ω×(0,T)⊂ ℝ^N+1. We study the local regularity properties for weak solutions in the subcritical range p≤(N(q+1))/(N+q+1) and 0<q<(N+2)/(N−2). Under an extra integrability assumption |u|∈ L_loc^rr(Ω_T), we establish a quantitative bound for |u|. Here, the exponent rr satisfies λ_rr=N(p−q−1)+prr>0. In addition, we prove local higher integrability of |Du| in the range p=(N(q+1))/(N+q+1) and (N+p)/(N−p)<q<(N+2)/(N−2), provided that |u|∈ L_loc^rr(Ω_T) holds.
ER -