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Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space

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Abstract

We study the nonexistence of solutions for fractional elliptic problems via a monotonicity result which obtained by the method of moving planes with an improved Aleksandrov–Bakelman–Pucci type estimate for the fractional Laplacian in unbounded domain.

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Acknowledgments

A.Q. was partially supported by Fondecyt Grant # 1110210 and Programa Basal, CMM. U. de Chile.

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Correspondence to Alexander Quaas.

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Communicated by A. Malchiodi.

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Quaas, A., Xia, A. Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space. Calc. Var. 52, 641–659 (2015). https://doi.org/10.1007/s00526-014-0727-8

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