Rocky Mountain Journal of Mathematics

Symmetry and monotonicity of solutions for equations involving the fractional Laplacian of higher order

Xuewei Cui and Weijie Song

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The aim of this paper is to establish symmetry and monotonicity of solutions to the equation involving fractional Laplacians of higher order. For this purpose, we first reduce the equation into a system via the composition of lower fractional Laplacians and then obtain symmetry and monotonicity of solutions to the system by applying the method of moving planes.

Article information

Rocky Mountain J. Math., Volume 48, Number 2 (2018), 485-499.

First available in Project Euclid: 4 June 2018

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Zentralblatt MATH identifier

Primary: 35B50: Maximum principles 35J60: Nonlinear elliptic equations 35S15: Boundary value problems for pseudodifferential operators

Fractional Laplacian of higher order ABP estimate radial symmetry monotonicity method of moving planes


Cui, Xuewei; Song, Weijie. Symmetry and monotonicity of solutions for equations involving the fractional Laplacian of higher order. Rocky Mountain J. Math. 48 (2018), no. 2, 485--499. doi:10.1216/RMJ-2018-48-2-485.

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