Well, that's not appropriate behavior on your 11 year olds part. Your partner should tell him that the 'silent treatment' is unacceptable and rude. And that he is not allowed to be rude to you. I believe kids can be mad and that a lot of step parents should be secondary in discipline to parents but a few instances of losing your temper and yelling, okay. It happens. No one is perfect. As the bio mom to my kids, I've lost my temper and yelled. I feel bad and regret it and apologize. That's life. But using silence as a weapon toward you is unacceptable behavior and it is time for your partner to step in for a teachable moment. Disrespect to anyone is not allowed.
Stop apologizing, stop paying much attention to it. Be friendly around the house and ignore how he is acting. And when he does begin to talk, make no big deal out of it and just move on. Then when you are a bit down the road, you can say "you know, I'm sorry that I yelled. I'm working on that." and leave it alone from there. But right now, he is not behaving appropriately. Your partner needs to step in.
good luck and let me know how it goes!