A note on the monotonicity of solutions for fractional equations in half-spaces
A note on the monotonicity of solutions for fractional equations in half-spaces
In this work we consider the nonlocal elliptic problem \begin{equation*} \left \{ \begin {array}{ll} (-\Delta )^s u = f(u) & \text {in } \mathbb {R}^N_+,\\[4pt] \ \ u=0 & \text {in } \mathbb {R}^N \setminus \mathbb {R}^N_+, \end{array} \right . \end{equation*} where $(-\Delta )^s$, $0<s<1$, stands for the fractional Laplacian …