$L^p$-regularity of a geometrically nonlinear system in supercritical dimensions

TL;DR

This paper extends the regularity results of a geometrically nonlinear Cosserat micropolar system from the critical to supercritical dimensions, establishing interior and sharp $L^p$ regularity.

Contribution

It provides new interior and $L^p$ regularity results for the Cosserat system in supercritical dimensions, building on prior work in the critical case.

Findings

Established interior regularity in supercritical dimensions

Proved sharp $L^p$ regularity for the system

Extended regularity results beyond the critical dimension

Abstract

In a recent work, Gastel and Neff introduced an interesting system from a geometrically nonlinear flat cosserat micropolar model and established interior regularity in the critical dimension. Inspired by their work on this flat Cosserat model, in this article, we establish both interior regularity and sharp $L^p$ regularity for their system in supercritical dimensions.