Journal of Function Spaces (Jan 2021)

Monotonicity and Symmetry of Solutions to Fractional Laplacian in Strips

  • Tao Sun,
  • Hua Su

DOI
https://doi.org/10.1155/2021/5354775
Journal volume & issue
Vol. 2021

Abstract

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In this paper, using the method of moving planes, we study the monotonicity in some directions and symmetry of the Dirichlet problem involving the fractional Laplacian −Δα/2ux=fux,x∈Ω,ux>0,x∈Ω,ux=0,x∈ℝn\Ω, in a slab-like domain Ω=ℝn−1×0,h⊂ℝn.