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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2106.11639 |
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| _version_ | 1866929420742164480 |
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| author | Chlebicka, Iwona Youn, Yeonghun Zatorska-Goldstein, Anna |
| author_facet | Chlebicka, Iwona Youn, Yeonghun Zatorska-Goldstein, Anna |
| contents | We study the existence of very weak solutions to a system \[\begin{cases}-\mathrm{div} \mathcal{A}(x,D\mathbf{u})=\mathbfμ\quad\text{in }\ Ω,
\mathbf{u}=0\quad\text{on }\ \partialΩ\end{cases} \]
with a datum $\mathbfμ$ being a vector-valued bounded Radon measure and $\mathcal{A}$ having measurable dependence on the spacial variable and Orlicz growth with respect to the second variable. We are {\em not} restricted to the superquadratic case.
For the solutions and their gradients we provide regularity estimates in the generalized Marcinkiewicz scale. In addition, we show a precise sufficient condition for the solution to be a~Sobolev function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_11639 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Measure data systems with Orlicz growth Chlebicka, Iwona Youn, Yeonghun Zatorska-Goldstein, Anna Analysis of PDEs We study the existence of very weak solutions to a system \[\begin{cases}-\mathrm{div} \mathcal{A}(x,D\mathbf{u})=\mathbfμ\quad\text{in }\ Ω, \mathbf{u}=0\quad\text{on }\ \partialΩ\end{cases} \] with a datum $\mathbfμ$ being a vector-valued bounded Radon measure and $\mathcal{A}$ having measurable dependence on the spacial variable and Orlicz growth with respect to the second variable. We are {\em not} restricted to the superquadratic case. For the solutions and their gradients we provide regularity estimates in the generalized Marcinkiewicz scale. In addition, we show a precise sufficient condition for the solution to be a~Sobolev function. |
| title | Measure data systems with Orlicz growth |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2106.11639 |