Timeline for Reference request – a priori estimate – mixed boundary condition
Current License: CC BY-SA 4.0
7 events
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| Apr 9, 2022 at 20:07 | comment | added | Beni Bogosel | @username: it turns out it is possible to obtain an estimate by integrating by parts by hand. It is weird that I couldn't find any explicit references regarding this. | |
| Mar 26, 2022 at 23:19 | comment | added | Beni Bogosel | @username: Thank you for your suggestions. Indeed, in Grisvard's book, there is a section on a priori estimates, where such kind of estimates is presented. However, it is in a very general setting, and in the case of the Laplacian, I thought there may be a more direct reference where the computations are more straightforward. I will try your second suggestion. | |
| Mar 26, 2022 at 16:14 | comment | added | username | Since your domain is convex, it is worth trying to do the calculation by hand, using Morawetz multipliers (testing against $\chi \cdot Du$ where $\chi$ is an extension of the normal vector into the interior) to check if you can't get simply $C=1$. | |
| Mar 26, 2022 at 16:10 | comment | added | username | In Grisvard's book, mixed boundary conditions is covered, as he considers a general boundary condition operator.. | |
| Mar 26, 2022 at 15:45 | history | edited | Beni Bogosel | CC BY-SA 4.0 |
added 86 characters in body
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| Mar 25, 2022 at 16:34 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tag
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| Mar 25, 2022 at 16:21 | history | asked | Beni Bogosel | CC BY-SA 4.0 |