Preprint
Inserted: 30 mar 2026
Last Updated: 30 mar 2026
Year: 2026
Abstract:
We revisit and refine the analysis of partial H\"older regularity for nondegenerate nonlinear elliptic systems in divergence form modeling stationary double-phase non-Newtonian fluids developed in https://cvgmt.sns.it/paper/5787/. The growth function is of the form $H(x,s)=s^p+\mu(x)s^q$, with $\tfrac{3n}{n+2}<p\le q$ and $\mu(\cdot)$ a nonnegative $C^{0,\alpha}$-continuous function for some $\alpha\in(0,1]$. Our main result establishes that the gradient $\nabla{\bf u}$ of any weak solution is locally Hölder continuous, except on a set of measure zero.
Keywords: Partial regularity, double-phase, Fluids
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