Timeline for Compactly-supported harmonic tensors
Current License: CC BY-SA 4.0
11 events
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| May 4, 2023 at 20:27 | comment | added | Liviu Nicolaescu | @RBega2 You are correct and I have deleted that embarrassing comment. The ad-hoc approach indicated by Rafe Mazzeo works. Aronszajn method works in this case. Rafe Mazzeo proves a Carleman inequality for generalized Laplacians in his paper "Unique continuation..." Amer. J. Math. 1991. This is all you need. | |
| May 2, 2023 at 22:12 | comment | added | RBega2 | @LiviuNicolaescu The result of Hormander requires an estimate on the absolute value of the Laplacian what you wrote only gives a one sided bound. | |
| May 1, 2023 at 17:15 | comment | added | RBega2 | Maybe this is simple but don't you need to be able to show that $|\nabla u|_E^2 \leq C |x|^{-1+\epsilon}|\nabla_M |u|^2|$ for some constants $C,\epsilon>0$ to apply Hormanders result? | |
| May 1, 2023 at 10:44 | comment | added | Liviu Nicolaescu | That is true. The only bit of good news for me at least is that in most geometric applications the operators involved are either of Dirac type or Laplacian type and unique continuation results are available in such cases. | |
| Apr 29, 2023 at 12:41 | comment | added | Igor Khavkine | Looking in from the outside, it's unfortunate that (to my knowledge) there doesn't appear to be a handy reference for (strong) unique continuation results for elliptic systems. If one doesn't know this trick of reducing to a scalar equation, or if it's not obviously applicable, the best options seems to be to start climbing up and down the citation tree from (Hile, Protter 1976) to see if the desired class of systems has been studied. | |
| Apr 29, 2023 at 8:44 | vote | accept | B.Hueber | ||
| Apr 28, 2023 at 18:06 | history | edited | Liviu Nicolaescu | CC BY-SA 4.0 |
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| Apr 28, 2023 at 17:56 | history | edited | Liviu Nicolaescu | CC BY-SA 4.0 |
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| Apr 28, 2023 at 14:04 | history | edited | Liviu Nicolaescu | CC BY-SA 4.0 |
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| Apr 28, 2023 at 11:30 | history | edited | Igor Khavkine | CC BY-SA 4.0 |
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| Apr 28, 2023 at 10:22 | history | answered | Liviu Nicolaescu | CC BY-SA 4.0 |