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arXiv · 2109.01026

Calderón-Zygmund-type estimates for singular quasilinear elliptic obstacle problems with measure data

Minh-Phuong Tran·Thanh-Nhan Nguyen·Phuoc-Nguyen Huynh
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Abstract

We deal with a global Calderón-Zygmund type estimate for elliptic obstacle problems of $p$-Laplacian type with measure data. For this paper, we focus on the singular case of growth exponent, i.e. $1<p \le 2-\frac{1}{n}$. In addition, the emphasis of this paper is in obtaining the Lorentz bounds for the gradient of solutions with the use of fractional maximal operators.

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Minh-Phuong Tran, Thanh-Nhan Nguyen, Phuoc-Nguyen Huynh. 2021-12-16. Calderón-Zygmund-type estimates for singular quasilinear elliptic obstacle problems with measure data. https://arxiv.org/abs/2109.01026

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