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An inhomogeneous wave equation and non-linear Diophantine approximation
Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review
- V. Beresnevich, University of York, United Kingdom
- M. M. Dodson, University of York, United Kingdom
- S. Kristensen
- J. Levesley, University of York, United Kingdom
- Department of Mathematical Sciences
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 |
|---|---|
| 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 |
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