An inhomogeneous wave equation and non-linear Diophantine approximation

V. Beresnevich, M. M. Dodson, S. Kristensen, J. Levesley

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    Abstract

    A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained.
    OriginalsprogEngelsk
    TidsskriftAdvances in Mathematics
    Vol/bind217
    Nummer2
    Sider (fra-til)740-760
    Antal sider21
    ISSN0001-8708
    DOI
    StatusUdgivet - 2008

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