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

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

We study Lp-theory of second-order elliptic divergence-type operators with measurable coefficients. To this end, we introduce a new method of constructing positive C0-semigroups on Lp associated with sesquilinear (not necessarily sectorial) forms in L2. A precise condition ensuring that the elliptic...

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Veröffentlicht in:Journal of functional analysis 2002-08, Vol.193 (1), p.24-54
Hauptverfasser: Sobol, Zeev, Vogt, Hendrik
Format: Artikel
Sprache:eng
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Zusammenfassung:We study Lp-theory of second-order elliptic divergence-type operators with measurable coefficients. To this end, we introduce a new method of constructing positive C0-semigroups on Lp associated with sesquilinear (not necessarily sectorial) forms in L2. A precise condition ensuring that the elliptic operator is associated with a quasi-contractive C0-semigroup on Lp is established.
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.2001.3908