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Lp-maximal regularity for second order Cauchy problems

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Abstract

We introduce the concept of Lp-maximal regularity for second order Cauchy problems. We prove Lp-maximal regularity for an abstract model problem and we apply the abstract results to prove existence, uniqueness and regularity of solutions for nonlinear wave equations.

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Author notes

  1. Ralph Chill

    Present address: Laboratoire de Mathématiques et Applications de Metz, UMR 7122, Université de Metz, Bât. A, lle du Saulcy, 57045, Metz Cedex 1, France

Authors and Affiliations

  1. Abteilung Angewandte Analysis, Universität Ulm, 89069, Ulm, Germany

    Ralph Chill

  2. Department of Mathematics, Lady Shri Ram College, Lajpat Nagar, New Delhi, India

    Sachi Srivastava

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  1. Ralph Chill
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  2. Sachi Srivastava
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Correspondence to Ralph Chill.

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The author acknowledges with thanks the support provided by the Department ofApplied Analysis, University of Ulm, and the travel grants provided by NBMH India and MSF Delhi, India.

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Chill, R., Srivastava, S. Lp-maximal regularity for second order Cauchy problems. Math. Z. 251, 751–781 (2005). https://doi.org/10.1007/s00209-005-0815-8

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