An inhomogeneous wave equation and non-linear Diophantine approximation

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

doi:10.1016/j.aim.2007.09.003

An inhomogeneous wave equation and non-linear Diophantine approximation

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

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

2 Citationer (Scopus)

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.

Originalsprog	Engelsk
Tidsskrift	Advances in Mathematics
Vol/bind	217
Nummer	2
Sider (fra-til)	740-760
Antal sider	21
ISSN	0001-8708
DOI	https://doi.org/10.1016/j.aim.2007.09.003
Status	Udgivet - 2008

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10.1016/j.aim.2007.09.003

Citationsformater

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title = "An inhomogeneous wave equation and non-linear Diophantine approximation",

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.",

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T1 - An inhomogeneous wave equation and non-linear Diophantine approximation

AU - Beresnevich, V.

AU - Dodson, M. M.

AU - Kristensen, S.

AU - Levesley, J.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

U2 - 10.1016/j.aim.2007.09.003

DO - 10.1016/j.aim.2007.09.003

M3 - Journal article

SN - 0001-8708

VL - 217

SP - 740

EP - 760

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 2

ER -

An inhomogeneous wave equation and non-linear Diophantine approximation

Abstract

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