An inhomogeneous wave equation and non-linear Diophantine approximation

TY - JOUR

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

AU - Beresnevich, Victor

AU - Dodson, M. M.

AU - Kristensen, Simon

AU - Levesley, Jason

PY - 2008/1/30

Y1 - 2008/1/30

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. (c) 2007 Elsevier Inc. All rights reserved.

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. (c) 2007 Elsevier Inc. All rights reserved.

KW - Diophantine approximation

KW - Hausdorff dimension

KW - wave equation

KW - small denominators problem

KW - Diophantine phenomena

KW - HAUSDORFF DIMENSION

KW - SOLVABILITY

KW - VECTORS

KW - FORMS

KW - SETS

UR - http://www.scopus.com/inward/record.url?scp=36048986413&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2007.09.003

DO - 10.1016/j.aim.2007.09.003

M3 - Article

VL - 217

SP - 740

EP - 760

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 2

ER -