# MathSciDoc: An Archive for Mathematician ∫

#### Analysis of PDEsmathscidoc:1701.03028

Arkiv for Matematik, 52, (2), 329-354, 2012.6
We obtain sharp integral potential bounds for gradients of solutions to a wide class of quasilinear elliptic equations with measure data. Our estimates are global over bounded domains that satisfy a mild exterior capacitary density condition. They are obtained in Lorentz spaces whose degrees of integrability lie below or near the natural exponent of the operator involved. As a consequence, nonlinear Calderón–Zygmund type estimates below the natural exponent are also obtained for $\mathcal{A}$ -superharmonic functions in the whole space ℝ^{$n$}. This answers a question raised in our earlier work (On Calderón–Zygmund theory for$p$- and $\mathcal{A}$ -superharmonic functions, to appear in$Calc. Var. Partial Differential Equations$, DOI10.1007/s00526-011-0478-8) and thus greatly improves the result there.
@inproceedings{nguyen2012global,
title={Global integral gradient bounds for quasilinear equations below or near the natural exponent},
author={Nguyen Cong Phuc},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203637628084061},
booktitle={Arkiv for Matematik},
volume={52},
number={2},
pages={329-354},
year={2012},
}

Nguyen Cong Phuc. Global integral gradient bounds for quasilinear equations below or near the natural exponent. 2012. Vol. 52. In Arkiv for Matematik. pp.329-354. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203637628084061.