On nondivergence form linear parabolic and elliptic equations with degenerate coefficients
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910133724905472 |
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| author | Dong, Hongjie Ryu, Junhee |
| author_facet | Dong, Hongjie Ryu, Junhee |
| contents | We establish the unique solvability in weighted mixed-norm Sobolev spaces for a class of degenerate parabolic and elliptic equations in the upper half space. The operators are in nondivergence form, with the leading coefficients given by $x_d^2a_{ij}$, where $a_{ij}$ is bounded, uniformly nondegenerate, and measurable in $(t,x_d)$ except $a_{dd}$, which is measurable in $t$ or $x_d$. In the remaining spatial variables, they have weighted small mean oscillations. In addition, we investigate the optimality of the function spaces associated with our results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_02286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On nondivergence form linear parabolic and elliptic equations with degenerate coefficients Dong, Hongjie Ryu, Junhee Analysis of PDEs 35J70, 35K65, 35D30, 35R05 We establish the unique solvability in weighted mixed-norm Sobolev spaces for a class of degenerate parabolic and elliptic equations in the upper half space. The operators are in nondivergence form, with the leading coefficients given by $x_d^2a_{ij}$, where $a_{ij}$ is bounded, uniformly nondegenerate, and measurable in $(t,x_d)$ except $a_{dd}$, which is measurable in $t$ or $x_d$. In the remaining spatial variables, they have weighted small mean oscillations. In addition, we investigate the optimality of the function spaces associated with our results. |
| title | On nondivergence form linear parabolic and elliptic equations with degenerate coefficients |
| topic | Analysis of PDEs 35J70, 35K65, 35D30, 35R05 |
| url | https://arxiv.org/abs/2509.02286 |