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

Du, Xusheng; Jin, Tianling; Xiong, Jingang; Yang, Hui

doi:10.1090/proc/16447

Blow up limits of the fractional Laplacian and their applications to the fractional Nirenberg problem
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by Xusheng Du, Tianling Jin, Jingang Xiong and Hui Yang;

Proc. Amer. Math. Soc. 151 (2023), 4693-4701

DOI: https://doi.org/10.1090/proc/16447

Published electronically: August 4, 2023

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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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