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

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

We prove that the operatorAu≔αu″, with α∈C[0,1] and α(x)>0 in (0,1), generates an analyticCo-semigroup onLp((0,1),1/α)≔{u∈Lp(0,1)||u|p/α∈L1(0,1)}, 1

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Veröffentlicht in:Journal of mathematical analysis and applications 1998-10, Vol.226 (2), p.393-413
Hauptverfasser: Goldstein, Gisèle R., Goldstein, Jerome A., Romanelli, Silvia
Format: Artikel
Sprache:eng
Schlagworte:
analytic semigroups
degenerate elliptic operators
interpolation between weighted-Lpspaces
Neuberger's Theorem
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Zusammenfassung:We prove that the operatorAu≔αu″, with α∈C[0,1] and α(x)>0 in (0,1), generates an analyticCo-semigroup onLp((0,1),1/α)≔{u∈Lp(0,1)||u|p/α∈L1(0,1)}, 1
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1998.6087