$L_p$-estimates for parabolic equations in divergence form with a half-time derivative
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929603217457152 |
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| author | Jung, Pilgyu Kim, Doyoon |
| author_facet | Jung, Pilgyu Kim, Doyoon |
| contents | We establish the unique solvability of solutions in Sobolev spaces to linear parabolic equations in a more general form than those in the literature. A distinguishing feature of our equations is the inclusion of a half-order time derivative term on their right-hand side. We anticipate that such equations will prove useful in various problems involving time evolution terms. Notably, the coefficients of the equations exhibit significant irregularity, being merely measurable with respect to the temporal variable or one spatial variable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L_p$-estimates for parabolic equations in divergence form with a half-time derivative Jung, Pilgyu Kim, Doyoon Analysis of PDEs 35K10, 35B65, 35R05 We establish the unique solvability of solutions in Sobolev spaces to linear parabolic equations in a more general form than those in the literature. A distinguishing feature of our equations is the inclusion of a half-order time derivative term on their right-hand side. We anticipate that such equations will prove useful in various problems involving time evolution terms. Notably, the coefficients of the equations exhibit significant irregularity, being merely measurable with respect to the temporal variable or one spatial variable. |
| title | $L_p$-estimates for parabolic equations in divergence form with a half-time derivative |
| topic | Analysis of PDEs 35K10, 35B65, 35R05 |
| url | https://arxiv.org/abs/2407.11305 |