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Loss of derivatives in evolution Cauchy problems

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Abstract

We study relations between modulus of continuity of the coefficients and loss of derivatives in the Cauchy problem for evolution operators with real characteristics in the Petrovsky sense. We also provide counterexamples to show that the obtained classification is sharp.

Keywords: Cauchy problem, Evolution equations, Loss of regularity of the solution

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Authors and Affiliations

  1. Facoltà di Ingegneria II, Via Genova 181, 47023 Cesena, Italy; Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40127 Bologna, Italy, Tel.: +39 547 339126, Fax: +39 547 339114,  

    Massimo Cicognani

  2. Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

    Ferruccio Colombini

Authors
  1. Massimo Cicognani
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  2. Ferruccio Colombini
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Cicognani, M., Colombini, F. Loss of derivatives in evolution Cauchy problems. Ann. Univ. Ferrara 52, 271–280 (2006). https://doi.org/10.1007/s11565-006-0020-7

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  • DOI: https://doi.org/10.1007/s11565-006-0020-7

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