$$L^{p}$$ L p -theory of elliptic differential operators with unbounded coefficients

Abstract

In this paper, we consider the generation of strongly continuous analytic semigroups on \(L^p((0,\omega ),\mu _{p}\, dx)\) and \(L^p((0,\omega ), dx), 1<p<\infty \), by a family of second order elliptic operators of the form Open image in new window As in [24], we shall prove the generation results on \(L^2\)-spaces using the sesquilinear forms. More general results are obtained by using interpolation procedure and Neuberger’s theorem.