Timeline for $\mathcal{C}^1(\overline{\Omega})$ gradient bounds for the Dirichlet problem of the heat equation on general domains
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Feb 8, 2022 at 16:14 | comment | added | username | The next standard source is Nicholas Alikakos. | |
| Feb 7, 2022 at 15:56 | comment | added | Theleb | This approach does not easily generalise for non-cylindrical domains, it is almost exclusively designed for analysis on cylinders. Thank you for your input though. | |
| Jan 28, 2022 at 20:02 | comment | added | username | The estimates for the standard (cylinder) problem are in Evans' PDE textbook. You can use the semigroup approach... | |
| Jan 28, 2022 at 15:11 | comment | added | Theleb | The differential operator still is the heat operator. Could you come up with a better name ? Actually the solvability of the Dirichlet problem on time evolving domains is well known (see the references), however I want more precise estimates near the boundary on the domain. | |
| Jan 28, 2022 at 11:58 | comment | added | username | So, you are considering a normal parabolic problem but instead of considering a problem on a cylinder, $\Omega=(0,T)\times \Omega$ you are considering a problem on a general smooth domain in time and space and that is where the problem resides. It isn't really the heat equation in that case, though.. | |
| Jan 28, 2022 at 10:24 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Added a reference section and correcteda a typo
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| Jan 28, 2022 at 8:48 | comment | added | Theleb | I edited the question, $\phi$ is assumed to be continuously differentiable. | |
| Jan 28, 2022 at 8:47 | history | edited | Theleb | CC BY-SA 4.0 |
added 17 characters in body
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| Jan 27, 2022 at 18:07 | history | edited | Jochen Wengenroth |
edited tags
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| Jan 27, 2022 at 16:26 | history | edited | Theleb | CC BY-SA 4.0 |
added 1 character in body
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| S Jan 27, 2022 at 14:31 | review | First questions | |||
| Jan 27, 2022 at 14:48 | |||||
| S Jan 27, 2022 at 14:31 | history | asked | Theleb | CC BY-SA 4.0 |