So, first things first: I hated District 9, and I hated this movie. Elaborating on either of those positions seems pretty dull to me, so I am going to try to do something that I don't have the background for at all: I'm going to try to discuss, despite an utter lack of technical knowledge (which I can sometimes fake), the opening shot of the movie, and why I think it spectacularly failed.
Elysium opens with a panoramic chopper tracking shot (see? I have no idea what I am talking about). Or rather, several; helicopters glide over future Los Angeles and the titular space station. This is meant, I assume, to achieve two ends: to orient the viewer in the secondary world (or future world, if you prefer), and (but also through) to present a striking juxtaposition. Wealth against poverty, visually coded in all those heavy ways that these thing tend to use as shorthand (the most obvious being white vs brown).
The aerial tracking shot manages to be simultaneously stabilizing and unsettling; it does the work of establishing without connoting stability. It uses the cinematic shorthand of objectivity, the aerial shot, as though a satellite or the sun itself, and makes it kinetic, smooth and quick.
The quickness of the shot is worth mentioning; despite the smooth tracking, it zooms over the ground in an uncanny way. This might have something to do with what people complain about when they talk about the difference between digital and film; a quick lookup of the film's technical specifications followed by a wikipedia search of the types of cameras used leads me to believe that it was shot on the Red Epic-X with the framerate dialed down, giving the impression of time lapse footage without the artifacts present in non-digital cameras; this would explain why, despite not looking as though there is any actual fast-forwarding going on, the camera appears to cover the ground much faster than one would expect a helicopter to allow for. The most obvious association, for me at least, is that this is what footage shot from a low-flying UAV might look like, if it were equipped with very high-end cameras. Thus the uncanniness of the whole thing.
In these opening shots is, in their way, the whole film. They're a sort of visual-technical objective correlative, an establishing frame which emphasizes the way that the film will concern itself with an apparently rigid hierarchical social construction that is nevertheless in motion; and how that motion, through the narrative, is conveyed through speed. If my assumption as to how it was filmed is correct (I wouldn't put too much credence in that though) there is another resonant dimension; the way that this speed is actually a kind of rehabilitated disjunctive slowness, that is, is formed not by acceleration but by deceleration, the shooting slowed to present quickness.
There is an obvious material explanation for why these shots don't linger; the film needs the ability to establish without stretching its run time. Regardless of the motivation, its aesthetics present themselves to the viewer as a sort of alienation from usual cinematic language; the most obvious counterpart is the Tarkovskian long shot, the most obvious example from Solaris. Consider, for instance, the steady series of aerial zoom outs that takes up the last minute and a half (roughly) of the movie; unlike the panning that begins Elysium, the speed of the shot seems less awkward due to the unsteady camera, and the fact that it moves away from, rather than over, its subject. I'm not a huge fan of Solaris (or that shot in particular) but it seems to me a good example of how something like Elysium uses that bizarre sped-up consistency to orient the viewer beyond in ways that exceed the ordinary language of film.
(Note: having since rewatched the opening scene, the only place where the speedy footage happens excessively are the shots over Elysium, not over (the film's) Los Angeles; this could be an interesting juxtaposition to follow but maybe I am wrong about that as well, or perhaps it is a digital artefact, or whatever else; basically I'm leaving this as is and someone who actually knows what they are talking about is free to run with it or call out my ignorance or whatever else.)