Nonlocal fractional elliptic equations and applications

Abstract

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