Need help in the Sicilian

What is black's best response after

 1. e4   ... c5  2. c3

The whole point with the Sicilian is to challenge white's center, but how do I prevent 3. d4? It seems like after 2. c3, there's no way to challenge that square anymore. Also, is this a common opening for white? it looks pretty strong (but maybe i'm missing something) 

 

thanks for any help.

This is called the Alapin Sicilian. There are a few ways for black to meet it.

 

 I think there was a Kasparov-Deep Blue game with the Alapin.

now you know that if deep-blue was programmed to play the Alapin against Kasparov is because Kasparov faced the Alapin only few times in his career losing to it as a young player when he was about 15 years old if I am not mistaking, and then showing signs of not being exactely at easy against this system later in his career, the Alapin system is a pain in the butt literaly, the best thing I have seen lately against the Alapin I think it was from Radjabov when he played 2...d5 3.exd Qxd5 and then he followed up with g6 fianchettoying his bishop at g7 immidiately, I have tryed many other systems against the Alapin and i never felt at easy with any of them, this Radjabov line i really like, I remember looking at this g6 line a while back and then giving it up thinking there was something there which could be not good for black

Among grandmasters Sveshnikov regular plays this variant for White.

The Black has 2 main continuations:

2. ... Nf6

2. ... d5

I believe that 2...Nf6 is the sharpest reply and what point is playing the Sicilian Defense if you don't play sharply?