Timeline for An estimate for the solution of an elliptic PDE depending on a parameter
Current License: CC BY-SA 3.0
17 events
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| Aug 11, 2017 at 12:03 | comment | added | Piero D'Ancona | The same argument works near any isolated point of the spectrum of an operator | |
| Aug 11, 2017 at 11:01 | history | edited | CooLee | CC BY-SA 3.0 |
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| Aug 11, 2017 at 11:00 | comment | added | CooLee | Here I assume $f$ is a fixed $L^2(\Omega)$-function. | |
| Jul 21, 2017 at 2:26 | history | edited | CooLee |
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| Jul 21, 2017 at 1:46 | comment | added | CooLee | Can the same argument work for the operator $-\Delta + \vec B\cdot \nabla$? | |
| Jul 20, 2017 at 20:24 | comment | added | Christian Remling | Since $u=(-\Delta-\lambda)^{-1}f$, the bound with a uniform $C$ and for all $f\in L^2$ would give the same uniform bound on $\|(-\Delta-\lambda)^{-1}\|$, which is impossible because the operator norm of the resolvent diverges when $\lambda$ approaches the spectrum (easy to show, from the spectral theorem). (The bound with a uniform $C$ for only specific $f$'s might conceivably hold.) | |
| Jul 20, 2017 at 15:32 | comment | added | Andrew | Wouldn't it lead to an a priory estimate in $W_2^2$ from which by the method of continuity would follow that the problem is solvable for $\lambda=\lambda_1$ for any $f\in L_2$? | |
| Jul 20, 2017 at 11:28 | history | edited | CooLee |
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| Jul 20, 2017 at 11:20 | history | edited | CooLee | CC BY-SA 3.0 |
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| Jul 20, 2017 at 9:32 | history | edited | CooLee | CC BY-SA 3.0 |
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| Jul 18, 2017 at 8:22 | history | edited | CooLee | CC BY-SA 3.0 |
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| Jul 17, 2017 at 7:03 | history | edited | CooLee | CC BY-SA 3.0 |
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| Jul 17, 2017 at 6:58 | history | edited | CooLee | CC BY-SA 3.0 |
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| Jul 16, 2017 at 12:46 | review | Close votes | |||
| Jul 16, 2017 at 15:47 | |||||
| Jul 16, 2017 at 10:07 | history | edited | CooLee | CC BY-SA 3.0 |
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| Jul 16, 2017 at 8:57 | history | edited | CooLee | CC BY-SA 3.0 |
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| Jul 16, 2017 at 8:46 | history | asked | CooLee | CC BY-SA 3.0 |