ANALYTIC SEMIGROUPS ON Lp w(0; 1) AND ON Lp(0; 1) GENERATED BY SOME CLASSES OF SECOND ORDER DIFFERENTIAL OPERATORS

Abstract

Of concern are singular ordinary dierential operators de- ned on an interval for which the coecient of ellipticity degenerates at the boundary of the interval. Thus, for instance, of concern is the operator A dened by Au := u00 + u0 on the interval (0; 1) where 2 C[0; 1]; $\gt $ 0 in (0; 1) and (0) = 0 = (1): We show that, in many cases, A (with suitable boundary conditions) generates a C0-semigroup on various (weighted or not) Lp spaces on (0; 1) which is analytic. It is the analyticity that is the focal point.