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arXiv · 2410.14350

Partial regularity for degenerate systems of double phase type

Jihoon Ok·Giovanni Scilla·Bianca Stroffolini
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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 H\"older continuous, except on a set of measure zero.

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Jihoon Ok, Giovanni Scilla, Bianca Stroffolini. 2024-10-18. Partial regularity for degenerate systems of double phase type. https://arxiv.org/abs/2410.14350

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