Nonlocal fractional elliptic equations and applications

Abstract

The Lp-coercive properties of a nonlocal fractional ellip tic equation is studied. Particularly, it is proved that the fractional elliptic operator generated by this equation is sec torial in Lp space and also is a generator of an analytic semigroup. Moreover, by using the Lp-separability proper ties of the given elliptic operator the maximal regularity of the corresponding nonlocal fractional parabolic equation is established.