$L^p$-Theory for Elliptic Operators on $\mathbb R^d$ with Singular Coefficients

Abstract

We study the generation of an analytic semigroup in L(R) and the determination of the domain for a class of second order elliptic operators with unbounded coefficients in R. We also establish the maximal regularity of type L–L for the corresponding inhomogeneous parabolic equation. In contrast to the previous literature the coefficients of the second derivatives are not required to be strictly elliptic or bounded. Interior singularities of the lower order terms are also discussed.