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arXiv · 2509.17031

Sharp Onofri trace inequality on the upper half space and quasi-linear Liouville equation with Neumann boundary

Jingbo Dou·Yazhou Han·Shuang Yuan·Yang Zhou
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Abstract

In this paper, we establish a sharp Onofri trace inequality on the upper half space $\overline{\mathbb R_+^n} (n\geq 2)$ by considering the limiting case of Sobolev trace inequality and classify its extremal functions on a suitable weighted Sobolev space. For this aim, by the Serrin-Zou type identity and the Pohozaev type identity, we show the classification of the solutions for a quasi-linear Liouville equation with Neumann boundary which is closely related to the Euler-Lagrange equation of the Onofri trace inequality and it has independent research value. The regularity and asymptotic estimates of solutions to the above equation are essential to discuss.

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Jingbo Dou, Yazhou Han, Shuang Yuan, Yang Zhou. 2025-09-21. Sharp Onofri trace inequality on the upper half space and quasi-linear Liouville equation with Neumann boundary. https://arxiv.org/abs/2509.17031

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