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You guessed right. That's a clearer description.
—Ben FrantzDale
Meaning
As far as I can tell, (or sometimes the square root thereof) can represent the energy of a configuration u (at least in the area of elasticity). The thing I can't figure out is this: what does when u and v are different configurations? I have a sense of what an inner product means between functions, but not in the energy space. Any thoughts?
—Ben FrantzDale05:56, 15 December 2006 (UTC)reply
Rewrite, and a question
I rewrote this article, primarily for style and to clarify things. I cut out the paragraph
That is, is that
linear functional which acts like B but has a domain of —that is, its domain includes all limit points, u, of the domain of B for which Bun is bounded as .
since it is not clear what norm one uses to talk about convergence and boundedness (the original norm, or the energy norm?).
Cool. I'll fix anything I see, but when I started this page it was at the edge of my understanding (hence the {{expert}} tag). Thanks.
—Ben FrantzDale02:33, 7 May 2007 (UTC)reply
Sounds good. I added a physical example. I must say physics is not my strength, I hope I got all right from Zeidler's book. Extra eyes to look over that would be very welcome of course.
Oleg Alexandrov (
talk)
03:56, 7 May 2007 (UTC)reply
Woah... Integration by parts
Oleg, I just had an ah-ha regarding this line of your example:
I guess. I don't know what "distributing the metric tensor across both arguments to the inner product" means, but I am glad it helped you.
Oleg Alexandrov (
talk)
05:05, 7 May 2007 (UTC)reply
It just means that I never liked this: . If it doesn't matter which side the B goes, it seems much more symmetrical to think of it as .
—Ben FrantzDale05:09, 7 May 2007 (UTC)reply