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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 11, 2021 at 23:49 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