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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2106.11639 |
| Etiquetas: |
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- 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.