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New thoughts on old results of R.T. Seeley

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In this paper we show that the L p -realization of a vector-valued elliptic boundary value problem (, j ) admits a bounded ∞-calculus on L p (G;E), 1<p<∞, provided the top-order coefficients of are Hölder continuous. Here G denotes a domain in n with compact C 2m-boundary and E a Banach space of class . Our proof is based on an abstract perturbation result for operators admitting bounded ∞-calculus and kernel estimates for the solution of (, j ).

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Authors and Affiliations

  1. Universiät Regensburg, Naturwissenschaftliche Fakultät I - Mathematik, D-93040, Regensburg, Germany

    Robert Denk

  2. Dipartimento di Matematica, Universita di Bologna, Piazza di Porta S. Donato 5, I-40127, Bologna, Italy

    Giovanni Dore

  3. Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289, Darmstadt, Germany

    Matthias Hieber

  4. Martin-Luther-Universität Halle-Wittenberg, Fachbereich Mathematik und Informatik, Institut Für Analysis, Theodor-Lieser-Strasse 5, D-06120 Halle, Germany

    Jan Prüss

  5. Dipartimento di Matematica, Universita di Bologna, Piazza di Porta S. Donato 5, I-40127, Bologna, Italy

    Alberto Venni

Authors
  1. Robert Denk
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  2. Giovanni Dore
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  3. Matthias Hieber
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  4. Jan Prüss
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  5. Alberto Venni
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Correspondence to Matthias Hieber.

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Mathematics Subject Classification (2000):35J45, 35K55

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Denk, R., Dore, G., Hieber, M. et al. New thoughts on old results of R.T. Seeley. Math. Ann. 328, 545–583 (2004). https://doi.org/10.1007/s00208-003-0493-y

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  • DOI: https://doi.org/10.1007/s00208-003-0493-y

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