A problem in non-linear Diophantine approximation

被引：1
|
作者：
Harrap, Stephen [1 ]
Hussain, Mumtaz [2 ]
Kristensen, Simon [3 ]
机构：
[1] Univ Durham, Dept Math Sci, Sci Labs, South Rd, Durham DH1 3LE, England
[2] La Trobe Univ, Dept Math & Stat, POB 199, Bendigo, Vic 3552, Australia
[3] Aarhus Univ, Dept Math, Ny Munkegade 118, DK-8000 Aarhus C, Denmark
来源：
NONLINEARITY | 2018年 / 31卷 / 04期
基金：
澳大利亚研究理事会;
关键词：
non-linear Diophantine approximation; partial differential equations; Hausdorff measure; Hausdorff dimension; Khintchine-Groshev theorem; HAUSDORFF DIMENSION; SOLVABILITY; THEOREM; SETS;
D O I：
10.1088/1361-6544/aaa498
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：1734 / 1756
页数：23
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