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Reading this article one gets the ideia that the Heat equation is also an Eliptic pde (the page elliptic partial differential equation redirects here), when it is in fact a Parabolic equation. Not knowing if the mention to the Heat equation in this page is correct (that is contains an Elliptic operator), could someone clarify it please? Jlsilva 11:26, 27 September 2007 (UTC)
There's nothing here about the properties of elliptic operators; it only covers the definitions. The page needs to review the basic properties of these operators, and say why these types of operators are so widespread and so useful. It also needs more links to specific examples of elliptic operators. Ewjw 09:07, 19 December 2005 (UTC)
I agree with the comment above; unless I knew what an elliptic operator was I wouldn't gain anything from the current version of the page. In particular, why is it called "elliptic"? What is elliptic about it? — BenFrantzDale 22:11, 17 February 2006 (UTC)
is not defined. What are these? Myrkkyhammas 21:53, 8 May 2007 (UTC)
I'm fairly new to this area of maths and came to this page after reading some of the first chapter of "Riemmanian Holonomy Groups and Calibrated Geometry" by Joyce. His definition of elliptic is that , so by continuity either positive definite or negative definite, not the claimed "iff positive definite" of this page. That seems to make sense since if P(u)=f is an expression of a positive definite equation -P(u)=-f is negative definite but just as valid.
Is this viable reasoning? All it needs is some mention of this choice in sign on the main page I think but it's a point which does need clarification. AlphaNumeric 20:06, 15 May 2007 (UTC)
This material is new for me. I cant understand anything from this article (and i do have some small background in analysis). just for example: "
where . Such an operator is called elliptic iff for every x the matrix of coefficients of the highest order terms"
this all passage is unclear to me, what is "i"? what is the meaning of ":"?
amit
I propose that it be split into two subarticles. The first, Elliptic operator, will focus on linear elliptic operators. There is a school of mathematics where "elliptic operator" means precisely that, and the article shall make clear from the outset that it will deal exclusively with the linear case. The other article will be Elliptic partial differential equation, which will deal with potentially nonlinear elliptic equations, and the typical analytic behavior one expects from solutions of such equations. I think the two areas of study are sufficiently distinct from one another that this should be done for the sake of clarity. The elliptic operators of Atiyah and Singer do not closely resemble those of Monge and Ampère. Silly rabbit ( talk) 12:32, 11 March 2008 (UTC)
This article appears to lack a definition of "elliptic operator." —Preceding unsigned comment added by 129.97.134.34 ( talk) 05:14, 8 July 2008 (UTC)
I don't understand why there is an in the . The symbol comes from taking Fourier Transforms and should not appear here. — Preceding unsigned comment added by Beowulf333 ( talk • contribs) 14:40, 7 November 2011 (UTC)
The comment(s) below were originally left at Talk:Elliptic operator/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
A major field of mathematics (redirect from elliptic partial differential equation.) Please adjust importance and class rating as needed. Silly rabbit 23:58, 11 June 2007 (UTC) |
Last edited at 23:58, 11 June 2007 (UTC). Substituted at 02:02, 5 May 2016 (UTC)