Fractional elliptic equations in nondivergence form: definition, applications and Harnack inequality

P. R. Stinga, M. Vaughan

We define the fractional powers $L^s=(-a^{ij}(x){\partial }_{ij}{)}^s$, $0<s<1$, of nondivergence form elliptic operators $L=-a^{ij}(x){\partial }_{ij}$ in bounded domains $Ω\subset\ma…