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arXiv · 2605.18235

Gradient estimates for singular elliptic measure data problems with double phase

Kyeong Song·Yeonghun Youn·Anna Zatorska-Goldstein
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Abstract

We consider elliptic measure data problems of the type \[ -\mathrm{div}\,(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du) = \mu \] in a bounded domain in $\mathbb{R}^n$, where $p<q$ and $a(\cdot) \ge 0$. We prove local Calder\'on--Zygmund estimates in the singular case $2-1/n < p < 2$, under natural assumptions on $p$, $q$ and $a(\cdot)$.

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Kyeong Song, Yeonghun Youn, Anna Zatorska-Goldstein. 2026-05-18. Gradient estimates for singular elliptic measure data problems with double phase. https://arxiv.org/abs/2605.18235

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