Abstract.

The regularity properties of nonlocal elliptic equations are investigated in abstract weighted Lp spaces. Here, we find sufficient conditions that guarantee the separability of the linear problems. We prove that the corresponding nonlocal elliptic operator is sectorial and is also a negative generator of an analytic semigroup. In application, the maximal regularity properties of the for degenerate abstract equation in Lp norms, and infinite systems of degenerate elliptic integro-differential equations with parameters are obtained.

Keywords:

sectorial operators, abstract weighted spaces, operator-valued multipliers, nonlocal equations, degenerate integro-differential equations