1. Introduction The mixed local and nonlocal operators L = − Δ + ( − Δ ) s emerge from the superposition of two stochastic processes with different scales; that is, the random walk and jump process [1,2], which is studied by many mathematicians. More precisely, Biagi et al. [3] established some qualitative property of solutions to the following mixed local and nonlocal elliptic problem: − Δ u ( x ) + ( − Δ ) s u ( x ) = f ( x ) , x ∈ Ω , u ( x ) ⩾ 0 , x ∈ Ω , u ( x ) = 0 , x ∈ R N ∖ Ω . Biagi et al.
