Optimal Regularity and Fredholm Properties of Abstract Parabolic Operators in Lp Spaces on the Real Line |
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Authors: | Giorgio Davide Di; Lunardi Alessandra; Schnaubelt Roland |
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Institution: | Dipartimento di Matematica, Università di Pisa Via Buonarroti 2, 56127 Pisa. Italy E-mail: digiorgi{at}mail.dm.unipi.it
Dipartimento di Matematica, Università di Parma Via D'Azeglio 85/A, 43100 Parma, Italy. E-mail: lunardi{at}unipr.it, http://math.unipr.it/~lunardi
FB Mathematik und Informatik, MartinLutherUniversität HalleWittenberg 06099 Halle, Germany. E-mail: schnaubelt{at}mathematik.uni-halle.de |
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Abstract: | We study the operator Lu(t):= u'(t) A(t) u(t) on Lp(R; X) for sectorial operators A(t), with t R, on a Banachspace X that are asymptotically hyperbolic, satisfy the AcquistapaceTerreniconditions, and have the property of maximal Lp-regularity.We establish optimal regularity on the time interval R showingthat L is closed on its minimal domain. We further give conditionsfor ensuring that L is a semi-Fredholm operator. The Fredholmproperty is shown to persist under A(t)-bounded perturbations,provided they are compact or have small A(t)-bounds. We applyour results to parabolic systems and to generalized OrnsteinUhlenbeckoperators. 2000 Mathematics Subject Classification 35K20, 35K90,47A53. |
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Keywords: | exponential dichotomies Lp-maximal regularity Fredholm operators |
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