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Mild well-posedness of vector-valued problems on the real line

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Abstract

We introduce the (W 1,p, L p)-mild well-posedness for the vector-valued problem u′ = Au + f on the real line \({\mathbb{R}}\) and give a characterization of this property by the L p-multiplier defined by the resolvent of the closed operator A.

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Authors and Affiliations

  1. Department of Mathematical Science, University of Tsinghua, Beijing, 100084, China

    Shangquan Bu

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  1. Shangquan Bu
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Correspondence to Shangquan Bu.

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This work was supported by the NSF of China and the Specialized Research Fund for the Doctoral Program of Higher Education.

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Bu, S. Mild well-posedness of vector-valued problems on the real line. Arch. Math. 95, 63–73 (2010). https://doi.org/10.1007/s00013-010-0134-0

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  • DOI: https://doi.org/10.1007/s00013-010-0134-0

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