A problem in non-linear Diophantine approximation

作者：Harrap Stephen^*; Hussain Mumtaz; Kristensen Simon

来源：Nonlinearity, 2018, 31(4): 1734-1756.

DOI：10.1088/1361-6544/aaa498

• non-linear Diophantine approximation
• partial differential equations
• Hausdorff measure
• Hausdorff dimension
• Khintchine-Groshev theorem

In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

• 出版日期2018-4