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arXiv · 2303.06979

Stein-Weiss type inequality on the upper half space and its applications

Xiang Li·Zifei Shen·Marco Squassina·Minbo Yang
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Abstract

In this paper, we establish some Stein-Weiss type inequalities with general kernels on the upper half space and study the existence of extremal functions for this inequality with the optimal constant. Furthermore, we also investigate the regularity, asymptotic estimates, symmetry and non-existence results of the positive solutions of the corresponding Euler-Lagrange integral system. As an application, we finally derive some Liouville type results for the Hartree type equations in the half space.

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Xiang Li, Zifei Shen, Marco Squassina, Minbo Yang. 2023-03-13. Stein-Weiss type inequality on the upper half space and its applications. https://arxiv.org/abs/2303.06979

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