Blow up limits of the fractional Laplacian and their applications to the fractional Nirenberg problem
Xusheng Du, Tianling Jin, Jingang Xiong, Hui Yang · Proceedings of the American Mathematical Society · 2023
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.