On the Interior $W^{1,p}$ estimate of extension problem of fractional   elliptic equation
  In order to study Fractional operator, Caffarelli introduced the concept of extension problem. Hence, for any fractional elliptic operator, we get a degenerate elliptic equation. By studying the W^{1,p} regularity of extension problem, we can get several L^p estimate of solution of original fractional elliptic equation. 
Junrong Yan
math.AP