论文标题
均质sobolev函数的无限限制的存在和唯一性
Existence and uniqueness of limits at infinity for homogeneous Sobolev functions
论文作者
论文摘要
我们在零模量家族以外的无限曲线沿无限曲线的限制的存在和独特性建立在同质索博莱夫空间中的功能，假设基础空间具有支持庞加莱不等式的双倍度量。我们还表征了该结论是不平凡的设置。其次，我们在度量测量空间上介绍了弱极坐标系和径向曲线的概念。然后给出了足够和必要的条件，以实现径向限制的存在。结果，我们表征了某些具体设置中径向极限的存在。
We establish the existence and uniqueness of limits at infinity along infinite curves outside a zero modulus family for functions in a homogeneous Sobolev space under the assumption that the underlying space is equipped with a doubling measure which supports a Poincaré inequality. We also characterize the settings where this conclusion is nontrivial. Secondly, we introduce notions of weak polar coordinate systems and radial curves on metric measure spaces. Then sufficient and necessary conditions for existence of radial limits are given. As a consequence, we characterize the existence of radial limits in certain concrete settings.
