Global Calderon-Zygmund theory for parabolic p-Laplacian system: the case 1 < p ≤ 2n/n+2

作者：Chen, Ke; Nguyen, Quoc-Hung^*; Zhao, Na

来源：Journal of Functional Analysis, 2023, 284(8): 109852.

DOI：10.1016/j.jfa.2023.109852

• Parabolic p -Laplacian system
• Calder?n-Zygmund theory

The aim of this paper is to establish global Calderon- Zygmund theory to parabolic p -Laplacian system: u(t) - div(| del mu vertical bar(p-2) del u) = div(|F|Fp-2) in omega x (0, T) subset of Rn+1, proving that F is an element of L-q double right arrow del u is an element of L-q, for any q > max{p, n(2-p) 2 } and p > 1. Acerbi and Mingione [2] proved this estimate in the case p > 2n n+2 . In this article we settle the case 1 < p <= 2n n+2 . We also treat systems with discontinuous coefficients having small BMO (bounded mean oscillation) norm.

• 单位
  复旦大学; 中国科学院