Wiener Regularity and Heat Semigroups on Spaces of Continuous Functions
作者： Wolfgang Arendt , Philippe Bénilan
DOI: 10.1007/978-3-0348-8765-6_3
关键词: Topological vector space 、 Equicontinuity 、 H-derivative 、 Dirichlet boundary condition 、 Elliptic operator 、 Compact-open topology 、 Dirichlet problem 、 Continuous linear operator 、 Mathematics 、 Pure mathematics
摘要: Let Ω ⊂ ℝ N be open. It is shown that the Dirichlet Laplacian generates a (holomorphic) C o-semigroup on o(Ω) if and only regular in sense of Wiener. The same result remains true for elliptic operators divergence form.
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sci-hub.st 参考文章(22)
Gunter Lumer, Luc Paquet, Semi-groupes holomorphes, produit tensoriel de semi-groupes et equations d’evolution Springer, Berlin, Heidelberg. pp. 156- 177 ,(1979) , 10.1007/BFB0071326
G. Lumer, Probleme de Cauchy et fonctions surharmoniques Lecture Notes in Mathematics. pp. 202- 218 ,(1976) , 10.1007/BFB0087580
Pascal Auscher, Louise Barthélemy, Philippe Bénilan, El Maati Ouhabaz, Absence de la L∞-contractivité pour les semi-groupes associés aux opérateurs elliptiques complexes sous forme divergence Potential Analysis. ,vol. 12, pp. 169- 189 ,(2000) , 10.1023/A:1008642508461
Wolfgang Arendt, Gaussian estimates and interpolation of the spectrum in $L^p$ Differential and Integral Equations. ,vol. 7, pp. 1153- 1168 ,(1994)
Frank Neubrander, Ulf Schlotterbeck, Ulrich Groh, Wolfgang Arendt, Rainer Nagel, Günther Greiner, Heinrich P. Lotz, Ulrich Moustakas, Annette Grabosch, One-parameter Semigroups of Positive Operators ,(1986)
Claude Tardif, Gaussian estimates for second order elliptic operators with boundary conditions Journal of Operator Theory. ,vol. 38, pp. 87- 130 ,(1997) , 10.1002/JGT.1025
Neil S Trudinger, David G Gilbarg, Elliptic Partial Differential Equations of Second Order ,(2018)
N.Th Varopoulos, Hardy-Littlewood theory for semigroups Journal of Functional Analysis. ,vol. 63, pp. 240- 260 ,(1985) , 10.1016/0022-1236(85)90087-4
H. F. Weinberger, W. Littman, G. Stampacchia, Regular points for elliptic equations with discontinuous coefficients Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze. ,vol. 17, pp. 43- 77 ,(1963)
Herbert Amann, Joachim Escher, Strongly continuous dual semigroups Annali di Matematica Pura ed Applicata. ,vol. 171, pp. 41- 62 ,(1996) , 10.1007/BF01759381