Not that I knew this, of course, but an elegy is "a mournful, melancholy, or plaintive poem, esp. a funeral song or a lament for the dead." That'll go a long way toward explaining the movie, which is about the fear of death (growing old more specifically), conscious selfishness, emotional unavailability, and a May-December romance between Sir Ben Kingsley and Penelope Cruz. Both are wonderful in their roles and they carry off the chemistry beautifully.
In sum, what I got out of this film experience was that men are bastards and it's frightening, as a guy, to see the lies -- big and small, to yourself and others -- that you can be capable of in certain situations. It all feels sickeningly familiar when thrown up on screen and highlighted, and you start to distrust yourself and hope that this isn't really something you can really relate to. But I could, and that was scary.
While the movie as a whole dragged a little bit at the end and I'd hoped for a better resolution, there are some wonderful lines in the movie and some real (ugly) truths to be discovered. Dennis Hopper steals every scene he's in, but that could partly be due to the fact that he has the lion's share of the funny/poignant lines. (Paraphrased) "Beautiful women are invisible because nobody ever really sees them."