Timeline for Sufficient conditions for an asymptotic compactness
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Feb 14, 2021 at 15:47 | history | edited | sharpe | CC BY-SA 4.0 |
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Feb 14, 2021 at 9:03 | answer | added | Jochen Wengenroth | timeline score: 0 | |
Feb 13, 2021 at 22:05 | history | edited | sharpe | CC BY-SA 4.0 |
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Feb 13, 2021 at 8:16 | comment | added | sharpe | @MaoWao Thank you for your comment. I modified the definition of the Dirichlet form. Do you know a nice condition to show the $L^2$ convergence? | |
Feb 13, 2021 at 8:15 | history | edited | sharpe | CC BY-SA 4.0 |
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Feb 13, 2021 at 6:07 | comment | added | MaoWao | a) Your definition of Dirichlet form is not complete, you additionally need $\mathcal{E}(f\wedge 1,f\wedge 1)\leq \mathcal{E}(f,f)$ (in fact, this makes you third bullet point superfluous). b) Your conditions are too weak. You could simply take $\mathcal{E}_n=\frac 1 n \mathcal{E}$, in which case your condition reduces to $\liminf_n \frac 1 n\mathcal{E}(u_n,u_n)<\infty$. Of course this is not strong enough to guarantee compactness in $L^2$ in general. | |
Feb 13, 2021 at 3:37 | history | edited | sharpe | CC BY-SA 4.0 |
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Feb 12, 2021 at 6:45 | history | edited | sharpe |
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Feb 12, 2021 at 1:27 | history | edited | sharpe | CC BY-SA 4.0 |
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Feb 11, 2021 at 23:49 | history | edited | sharpe | CC BY-SA 4.0 |
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Feb 11, 2021 at 23:14 | history | edited | sharpe | CC BY-SA 4.0 |
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Feb 11, 2021 at 22:05 | history | edited | sharpe | CC BY-SA 4.0 |
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Feb 11, 2021 at 21:57 | history | asked | sharpe | CC BY-SA 4.0 |