论文标题
$ p $ -superminimizers的逆变和全球结果
Convergence and local-to-global results for $p$-superminimizers on quasiopen sets
论文作者
论文摘要
在本文中，获得了公制空间中的准蛋白套装上的精细$ p $ - （超级）最小化器的几个收敛结果。为此，我们推断出$ p $ - （超级）的cAccioppoli型不平等和局部到全球原则。这些考虑因素的重要部分是表明该功能属于合适的局部罚款Sobolev空间。我们证明了一个完整的度量空间，配备了两倍的度量，支持$ p $-poincaré不平等，$ 1 <p <\ p <\ infty $。但是，大多数结果也是未加权的$ \ mathbf {r}^n $的新结果。
In this paper, several convergence results for fine $p$-(super)minimizers on quasiopen sets in metric spaces are obtained. For this purpose, we deduce a Caccioppoli-type inequality and local-to-global principles for fine $p$-(super)minimizers on quasiopen sets. A substantial part of these considerations is to show that the functions belong to a suitable local fine Sobolev space. We prove our results for a complete metric space equipped with a doubling measure supporting a $p$-Poincaré inequality with $1<p< \infty$. However, most of the results are new also for unweighted $\mathbf{R}^n$.
