I happen to play trombone and tuba, and have done some research into soundproofing, hoping to promote harmony in my family.
The only effective soundproofing for sounds below 400 HZ or so is VERY expensive and involved. You have to either completely enclose the quiet room or completely enclose the sound source. Among other requirements, these enclosures have to actually isolate the interior walls, ceiling, and floor so that there is hardly any physical contact, and must be air tight. Since the floor has to sit on something, complete isolation is impossible. The only really successful compromise is to place the soundproof room directly on the ground. Even if the other requirements were possible for you, this one probably blows you out of the water.
The problem is that low frequencies have a long wavelength, which allows the waves to travel around obstacles and through spaces, even very small ones. They also travel very efficiently through solid materials, like wood and concrete. You can dampen and diffuse the sound by hanging blankets or carpet pad on the back wall of the closet to take out the high frequencies (which are always present, even in sounds that seem to be low frequency) but I'd suggest you give up on getting your place soundproofed.
I can think of a couple of other alternatives to make your life more pleasant. I assume your greatest problem is getting to sleep. You might look into 'white noise' generators. These make a quiet, broad frequency 'Shhh' sound that covers other noises but which the brain will ignore as 'background noise', so it is unobtrusive. Another, easier alternative would be to go to sleep with soft music playing. A third possibility might be to find an apartment farther from the elevator.
I wish I could be encouraging about your chances of soundproofing, but it is VERY tough to eliminate low frequencies. Good luck!