Published Paper

Inserted: 18 oct 2024
Last Updated: 10 mar 2025

Journal: Journal of Differential Equations
Volume: 432
Pages: 113207
Year: 2025
Doi: 10.1016/j.jde.2025.02.078

Abstract:

We study partial regularity for degenerate elliptic systems of double-phase type, where the growth function is given by $H(x,t)=t^p+a(x)t^q$ with $1<p\leq q$ and $a(x)$ a nonnegative $C^{0,\alpha}$-continuous function. Our main result proves that if $\frac{q}{p}\leq 1+\frac{\alpha}{n}$, the gradient of any weak solution is locally Hölder continuous, except on a set of measure zero.

Keywords: Partial regularity, double phase, degenerate system, harmonic approximation

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