Riesz potential estimates for mixed local-nonlocal problems with measure data
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917562653081600 |
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| author | Chlebicka, Iwona Song, Kyeong Youn, Yeonghun Zatorska-Goldstein, Anna |
| author_facet | Chlebicka, Iwona Song, Kyeong Youn, Yeonghun Zatorska-Goldstein, Anna |
| contents | We study gradient regularity for mixed local-nonlocal problems modelled upon \[ -Δ_p u +(-Δ_p)^su=μ\qquad\text{for} \quad 2-\tfrac{1}{n}<p<\infty\quad \text{and}\quad s\in(0,1)\,,\] where $μ$ is a bounded Borel measure. We prove pointwise bounds for the gradient $Du$ in terms of the truncated 1-Riesz potential of $μ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04549 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Riesz potential estimates for mixed local-nonlocal problems with measure data Chlebicka, Iwona Song, Kyeong Youn, Yeonghun Zatorska-Goldstein, Anna Analysis of PDEs We study gradient regularity for mixed local-nonlocal problems modelled upon \[ -Δ_p u +(-Δ_p)^su=μ\qquad\text{for} \quad 2-\tfrac{1}{n}<p<\infty\quad \text{and}\quad s\in(0,1)\,,\] where $μ$ is a bounded Borel measure. We prove pointwise bounds for the gradient $Du$ in terms of the truncated 1-Riesz potential of $μ$. |
| title | Riesz potential estimates for mixed local-nonlocal problems with measure data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.04549 |