Asymptotic approach to singular solutions for the CR Yamabe equation

Giampiero Palatucci; Mirco Piccinini

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arXiv · 2307.14933

Asymptotic approach to singular solutions for the CR Yamabe equation

Giampiero Palatucci·Mirco Piccinini

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Abstract

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 Kor\'any 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.

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Giampiero Palatucci, Mirco Piccinini. 2023-07-27. Asymptotic approach to singular solutions for the CR Yamabe equation. https://arxiv.org/abs/2307.14933

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