论文标题
Carnot组的Sobolev映射和模量不平等
Sobolev mappings and moduli inequalities on Carnot groups
论文作者
论文摘要
在文章中，我们研究了Carnot组的映射满足模量不平等。我们证明，同构具有带有本地集成函数$ q $的模量不平等（$ q $ -Homeomor \ - phisms）是Sobolev映射。在弱反映射定理的框架内，我们证明，映射与类$ w^1_ {c {c {c}}}（ω;ω;ω;ω''$的sobolev同态构态构图均属于sobolev class $ w^1_ class $ w^1_ {1，
In the article we study mappings of Carnot groups satisfy moduli inequalities. We prove that homeomorphisms satisfy the moduli inequalities ($Q$-homeomor\-phisms) with a locally integrable function $Q$ are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem we prove that mappings inverse to Sobolev homeomorphisms of finite distortion of the class $W^1_{ν,\text{loc}}(Ω;Ω')$ belong to the Sobolev class $W^1_{1,\text{loc}}(Ω';Ω)$.
