Analytic semigroups on Lpw(0, 1) and on Lp(0, 1) generated by some classes of second order differential operators


Of concern are singular ordinary differential operators defined on an interval for which the coefficient of ellipticity degenerates at the boundary of the interval. Thus, for instance, of concern is the operator A defined by Au := αu″+ βszlig;u′ on the interval (0, 1) where α ∈ C[0, 1], α > 0 in (0, 1) and α(0) = 0 = α(1). We show that, in many cases, A (with suitable boundary conditions) generates a Co-semigroup on various (weighted or not) Lp spaces on (0, 1) which is analytic. It is the analyticity that is the focal point.

Publication Title

Taiwanese Journal of Mathematics