A New Approach to the Analyticity of Some Classes of One-Parameter Semigroups in Weighted-Lp Spaces

Author： Goldstein G.R.   Goldstein J.A.   Ames S.W.F.  

Publisher： Academic Press

ISSN： 0022-247X

Source： Journal of Mathematical Analysis and Applications, Vol.226, Iss.2, 1998-10, pp. : 393-413

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Abstract

We prove that the operator Au ≔ αu″, with α ∈ C[0, 1] and α(x) > 0 in (0, 1), generates an analytic Co-semigroup on Lp((0, 1), 1/α) ≔ {u ∈ Lp(0, 1)| |u|p/α ∈ L1(0, 1)}, 1 < p < ∞, provided that some additional assumptions depending on the domain of A are required for α. The main tools used here are J. Neuberger's sufficient condition for analyticity and the Stein Interpolation Theorem.

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