Singular-degenerate parabolic systems with the conormal boundary condition on the upper half space
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914583880400896 |
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| author | Bekmaganbetov, Bekarys Dong, Hongjie |
| author_facet | Bekmaganbetov, Bekarys Dong, Hongjie |
| contents | We prove the well-posedness and regularity of solutions in mixed-norm weighted Sobolev spaces for a class of second-order parabolic and elliptic systems in divergence form in the half-space $\mathbb{R}^d_+ = \{x_d > 0\}$ subject to the conormal boundary condition. Our work extends results previously available for scalar equations to the case of systems of equations. The leading coefficients are the product of $x_d^α$ and bounded non-degenerate matrices, where $α\in (-1,\infty)$. The leading coefficients are assumed to be merely measurable in the $x_d$ variable, and to have small mean oscillations in small cylinders with respect to the other variables. If the parameter $α>0$, the lower-order coefficients are allowed to blow-up near the boundary. Our results readily generalize to infinite-dimensional equations in general real and complex Hilbert spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18418 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singular-degenerate parabolic systems with the conormal boundary condition on the upper half space Bekmaganbetov, Bekarys Dong, Hongjie Analysis of PDEs 35K40, 35K65, 35K67, 35D30, 46E40 We prove the well-posedness and regularity of solutions in mixed-norm weighted Sobolev spaces for a class of second-order parabolic and elliptic systems in divergence form in the half-space $\mathbb{R}^d_+ = \{x_d > 0\}$ subject to the conormal boundary condition. Our work extends results previously available for scalar equations to the case of systems of equations. The leading coefficients are the product of $x_d^α$ and bounded non-degenerate matrices, where $α\in (-1,\infty)$. The leading coefficients are assumed to be merely measurable in the $x_d$ variable, and to have small mean oscillations in small cylinders with respect to the other variables. If the parameter $α>0$, the lower-order coefficients are allowed to blow-up near the boundary. Our results readily generalize to infinite-dimensional equations in general real and complex Hilbert spaces. |
| title | Singular-degenerate parabolic systems with the conormal boundary condition on the upper half space |
| topic | Analysis of PDEs 35K40, 35K65, 35K67, 35D30, 46E40 |
| url | https://arxiv.org/abs/2509.18418 |