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arXiv · 2112.00960

Blow up limits of the fractional Laplacian and their applications to the fractional Nirenberg problem

Xusheng Du·Tianling Jin·Jingang Xiong·Hui Yang
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Abstract

We show a convergence result of the fractional Laplacian for sequences of nonnegative functions without uniform boundedness near infinity. As an application, we construct a sequence of solutions to the fractional Nirenberg problem that blows up in the region where the prescribed functions are negative. This is a different phenomenon from the classical Nirenberg problem.

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Xusheng Du, Tianling Jin, Jingang Xiong, Hui Yang. 2021-12-02. Blow up limits of the fractional Laplacian and their applications to the fractional Nirenberg problem. https://arxiv.org/abs/2112.00960

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