Asymptotic approach to singular solutions for the CR Yamabe equation

We study the loss of compactness for optimal functions of a subcritical approximations of the sharp Folland-Stein-Sobolev embedding in the Heisenberg group.

When blow-up is prevent at the boundary we show that centered-symmetric maximizers in a Korány ball concentrate at its center.

Moreover, we obtain the exact blow-up rate and the pointwise asymptotic profile away from the pole, in turn establishing a natural counterpart of the classical Brezis and Peletier asymptotics for nearly critical Sobolev problems.