On the singular p-Laplacian system under Navier slip type boundary conditions. The gradient-symmetric case

TL;DR

This paper establishes boundary regularity results for a p-Laplacian system with symmetric gradient under Navier slip conditions, including the singular case, advancing understanding of fluid-like systems with non-Newtonian behavior.

Contribution

It proves W^{2, q} regularity up to the boundary for the p-Laplacian system with symmetric gradient and Navier slip conditions, including the singular case p=1.

Findings

W^{2, q} regularity up to the boundary achieved

Regularity results valid for the singular case =0

Applicable for 1< p = 2 and suitable q

Abstract

We consider the p-Laplacian system of N equations in n space variables, 1< p\leq 2, under the homogeneous Navier slip boundary condition. Furthermore, the gradient of the velocity is replaced by the, more physical, symmetric gradient. We prove W^{2, q} regularity, up to the boundary, under suitable assumptions on the couple p,q. The singular case \mu= 0 is covered.