Perturbation theorems for maximal L_p-regularity

• Peer Christian Kunstmann ^[1] ; Lutz Weis ^[1]
  1. [1] Universität Karlsruhe, Germany
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 30, Nº 2, 2001, págs. 415-435
• Idioma: inglés
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• Resumen

  • In this paper we prove perturbation theorems for R-sectorial operators.

    Via the characterization of maximal Lp-regularity in terms of R-boundedness due to the second author we obtain perturbation theorems for maximal Lp-regularity in UMD -spaces. We prove that R-sectoriality of A is preserved by A-small perturbations and by perturbations that are bounded in a fractional scale and small in a certain sense. Here, our method seems to give new results even for sectorial operators.

    We apply our results to uniformly elliptic systems with bounded uniformly continuous coefficients, to Schr6dinger operators with bad potentials, to the perturbation of boundary conditions, and to pseudo-differential operators with non-smooth symbols.