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Sep 17, 2011 at 21:09 comment added dranxo When you perturb your operator (eg by coarsening the grid) how the spectrum changes can be studied with a differential equation. terrytao.wordpress.com/2008/10/28/when-are-eigenvalues-stable might be useful.
Sep 17, 2011 at 15:09 comment added alext87 Yes, you are right. I have no idea how to show this then. :(
Sep 17, 2011 at 15:05 history edited alext87 CC BY-SA 3.0
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Sep 17, 2011 at 14:41 comment added Denis Serre I don't understand why the inequality of your attempt should be true. The right-hand side should involve some norm of $u$ (that in $L^2$ maybe) and the inequality can be valid only for special $u$'s, because $u\mapsto u(x_j)$ is not well-defined on $L^2$.
Sep 17, 2011 at 14:38 history edited Denis Serre CC BY-SA 3.0
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Sep 17, 2011 at 11:18 history edited alext87 CC BY-SA 3.0
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Sep 17, 2011 at 11:10 history asked alext87 CC BY-SA 3.0