On the Lp-Theory of C0-Semigroups Associated with Second-Order Elliptic Operators, II

✍ Scribed by Vitali Liskevich; Zeev Sobol; Hendrik Vogt

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 239 KB
• Volume: 193
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2001.3909

✦ Synopsis

We study positive C 0 -semigroups on L p associated with second-order uniformly elliptic divergence-type operators with singular lower-order terms, subject to a wide class of boundary conditions. We obtain an interval ðp min ; p max Þ in the L p -scale where these semigroups can be defined, including the case 2 = 2 ðp min ; p max Þ. We present an example showing that the result is optimal. We also show that the semigroups are analytic with angles of analyticity and spectra of the generators independent of p, for the whole range of p where the semigroups are defined.