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

Hui Yang; Jingang Xiong; Tianling Jin; Xusheng Du

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

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arxiv 2112.00960 v1 pith:ZVUJ7ENX submitted 2021-12-02 math.AP

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

Xusheng Du , Tianling Jin , Jingang Xiong , Hui Yang This is my paper

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keywords fractionalnirenbergproblemfunctionslaplacianapplicationapplicationsblow

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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.

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

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