TY - JOUR
AU - Tran, N.-T.-Nhu
AB - We investigate the global regularity for weak solutions to a generalized stationary Stokes problem with BMO coefficients in a non-smooth domains. The results in this paper fall into two categories to get estimates for both velocity gradient and its associated pressure, corresponding to the two classes of generalized function spaces. Our first outcome is the generalized Lorentz spaces Λν,ωs,t(Ω)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Lambda _{\nu ,\omega }^{s,t}(\Omega )$$\end{document} estimate with Muckenhoupt weights. The second concerns a global bound in ψ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\psi $$\end{document}-generalized Morrey spaces Ms,ψ(Ω)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {M}^{s,\psi }(\Omega )$$\end{document}. The proof technique in our study is an adaption of innovative method launched in Acerbi and Mingione (Duke Math J 136(2):285–320, 2007), and distinctive feature is that we employ the so-called fractional maximal distribution functions.
TI - Regularity estimates for stationary Stokes problem in some generalized function spaces
JF - Zeitschrift für angewandte Mathematik und Physik
DO - 10.1007/s00033-022-01901-x
DA - 2023-02-01
UR - https://www.deepdyve.com/lp/springer-journals/regularity-estimates-for-stationary-stokes-problem-in-some-generalized-TYYDcpXYxX
VL - 74
IS - 1
DP - DeepDyve
ER -