Title: $L^p$-regularity of a geometrically nonlinear flat Cosserat micropolar model in supercritical dimensions

Abstract: In a recent work [Ann. Inst. H. Poincar\'e C Anal. Non Lin\'eaire 2024], Gastel and Neff introduced an interesting system from a geometrically nonlinear flat cosserat micropolar model and established interior regularity in the critical dimension. Motived by this work, in this article, we establish both interior regularity and sharp $L^p$ regularity for their system in supercritical dimensions.