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

✍ Scribed by Zeev Sobol; Hendrik Vogt

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 297 KB
Volume: 193
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3908

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✦ Synopsis

We study L p -theory of second-order elliptic divergence-type operators with measurable coefficients. To this end, we introduce a new method of constructing positive C 0 -semigroups on L p associated with sesquilinear (not necessarily sectorial) forms in L 2 . A precise condition ensuring that the elliptic operator is associated with a quasi-contractive C 0 -semigroup on L p is established.

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On the Lp-Theory of C0-Semigroups Associ

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

✍ Vitali Liskevich; Zeev Sobol; Hendrik Vogt 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 239 KB

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, includin