Timeline for Linear elliptic problems: Are gradient estimates preserved after perturbation?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 28, 2023 at 14:54 | comment | added | Hannes | @Muschkopp But now the assumptions for $B$ are also so strong that your desired estimate follows from the Gilbarg/Trudinger Chapter anyway, no? :-) | |
| Mar 27, 2023 at 7:47 | comment | added | Muschkopp | @Hannes I was thinking of an a priori argument (assuming you have bounds for $u$ do they also hold for $v$) but I have now updated the question to ensure the regularity for $u$ | |
| Mar 27, 2023 at 7:44 | comment | added | Muschkopp | @sorrymaker symmetry is not the issue for me, I am fine with assuming it (I have updated the question accordingly) | |
| Mar 27, 2023 at 7:43 | history | edited | Muschkopp | CC BY-SA 4.0 |
fixed the regularity assumptions in accordance to the comments
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| Mar 26, 2023 at 11:57 | comment | added | Hannes | This will be very hard to say since your assumptions are in general not strong enough to give bounded solution gradients for any matrix $A$ and data $f$ with the stated properties, so you either need to strengthen these accordingly (see e.g. Gilbarg/Trudinger Chapter 8.11) or you need to tell about the particularities of the given $A$ and $f$. | |
| Mar 25, 2023 at 8:04 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tag
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| Mar 25, 2023 at 3:07 | comment | added | sorrymaker | What method do you use to estimate the gradient for $u$? Is the problem a result of the lack of symmetry in $B$? | |
| Mar 22, 2023 at 16:54 | history | asked | Muschkopp | CC BY-SA 4.0 |