On solvability in the small of higher order elliptic equations in Orlicz-Sobolev spaces
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917574982238208 |
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| author | Asadzade, Javad A. |
| author_facet | Asadzade, Javad A. |
| contents | In this article, we consider a higher-order elliptic equation with nonsmooth coefficients with respect to Orlicz spaces on the domain $Ω\subset\mathbb{R}^{n}$. The separable subspace of this space is distinguished in which infinitely differentiable and compactly supported functions are dense; Sobolev spaces generated by these subspaces are determined. We demonstrate the local solvability of the equation in Orlicz-Sobolev spaces under specific restrictions on the coefficients of the equation and the Boyd indices of the Orlicz space. This result strengthens the previously known classical $L_{p}$ analog. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05643 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On solvability in the small of higher order elliptic equations in Orlicz-Sobolev spaces Asadzade, Javad A. Analysis of PDEs In this article, we consider a higher-order elliptic equation with nonsmooth coefficients with respect to Orlicz spaces on the domain $Ω\subset\mathbb{R}^{n}$. The separable subspace of this space is distinguished in which infinitely differentiable and compactly supported functions are dense; Sobolev spaces generated by these subspaces are determined. We demonstrate the local solvability of the equation in Orlicz-Sobolev spaces under specific restrictions on the coefficients of the equation and the Boyd indices of the Orlicz space. This result strengthens the previously known classical $L_{p}$ analog. |
| title | On solvability in the small of higher order elliptic equations in Orlicz-Sobolev spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2308.05643 |