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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.09087 |
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| _version_ | 1866915849491709952 |
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| author | Li, Ying Zhang, Chao |
| author_facet | Li, Ying Zhang, Chao |
| contents | We establish gradient estimates of solutions to a class of nonlinear elliptic equations with measure data under Orlicz-type growth conditions. The growth is governed by the structural condition \[ 0<i_a\le t g'(t)/g(t)\le s_a<1. \] We obtain two types of regularity results: pointwise Wolff potential estimates for the gradient of solutions in the singular regime $i_a \in \big(\frac{n-1}{2n-1},1\big)$, and Lipschitz regularity of the solutions in the regime $i_a \in (0,1)$. In the power-type case $g(t)=t^{p-1}$, our results recover the known gradient estimates for the singular $p$-Laplace equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09087 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gradient estimates for nonlinear elliptic equations with Orlicz growth and measure data Li, Ying Zhang, Chao Analysis of PDEs We establish gradient estimates of solutions to a class of nonlinear elliptic equations with measure data under Orlicz-type growth conditions. The growth is governed by the structural condition \[ 0<i_a\le t g'(t)/g(t)\le s_a<1. \] We obtain two types of regularity results: pointwise Wolff potential estimates for the gradient of solutions in the singular regime $i_a \in \big(\frac{n-1}{2n-1},1\big)$, and Lipschitz regularity of the solutions in the regime $i_a \in (0,1)$. In the power-type case $g(t)=t^{p-1}$, our results recover the known gradient estimates for the singular $p$-Laplace equation. |
| title | Gradient estimates for nonlinear elliptic equations with Orlicz growth and measure data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.09087 |