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.
Original language | English |
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Journal | Advances in Mathematics |
Volume | 217 |
Issue | 2 |
Pages (from-to) | 740-760 |
Number of pages | 21 |
ISSN | 0001-8708 |
DOIs | |
Publication status | Published - 2008 |