Calculus of Variations and Geometric Measure Theory

G. Scilla - B. Stroffolini

Orlicz meets double phase: steady fluids

created by scilla on 30 Mar 2026

[BibTeX]

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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