Overdetermined Elliptic Systems
Overdetermined Elliptic Systems
复制标题
超定椭圆系统
DOI：
--
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发表时间：
2003
影响因子：
3
通讯作者：
J. Tuomela
中科院分区：
文献类型：
--
作者：
Katsiaryna Krupchyk;W. Seiler;J. Tuomela
摘要我们考虑线性超定偏微分方程组。
我们表明，权重的引入经典地用于定义
椭圆度是不必要的，因为任何系统都是椭圆的
在完成到的过程中，某些权重变为不带权重的椭圆
内卷曲。此外，事实证明，有些系统并不是
对于任何权重的选择是椭圆的，但其对合形式仍然是
椭圆形的。我们还证明了将给定的系统降阶或降阶
只有一个未知函数的等价系统保持椭圆性。
AbstractWe consider linear overdetermined systems of partial differential equations.
We show that the introduction of weights classically used for the definition
of ellipticity is not necessary, as any system that is elliptic with respect
to some weights becomes elliptic without weights during its completion to
involution. Furthermore, it turns out that there are systems which are not
elliptic for any choice of weights but whose involutive form is nevertheless
elliptic. We also show that reducing the given system to lower order or to
an equivalent system with only one unknown function preserves ellipticity.