Fractional $p$-Laplacians via Neumann problems in unbounded metric
measure spaces
Fractional $p$-Laplacians via Neumann problems in unbounded metric
measure spaces
We prove well-posedness, Harnack inequality and sharp regularity of solutions to a fractional $p$-Laplace non-homogeneous equation $(-\Delta_p)^su =f$, with $0<s<1$, $1<p<\infty$, for data $f$ satisfying a weighted $L^{p'}$ condition in a doubling metric measure space $(Z,d_Z,\nu)$ that is possibly unbounded. Our approach is inspired by the work of Caffarelli and …