Monotonicity and Symmetry of Solutions to Fractional Laplacian in Strips
Tao Sun, Hua Su · Journal of Function Spaces · 2021
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 − Δ α / 2 u x = f u x , x ∈ Ω , u x > 0 , x ∈ Ω , u x = 0 , x ∈ ℝ n \ Ω , in a slab-like domain Ω = ℝ n − 1 × 0 , h ⊂ ℝ n .