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Morrey's fractional integrals in Campanato-Sobolev's space and divF = f
Journal de Mathématiques Pures et Appliquées ( IF 2.1 ) Pub Date : 2020-08-24 , DOI: 10.1016/j.matpur.2020.08.005
Liguang Liu , Jie Xiao

The purpose of this paper is three-fold: the first is to determine the Campanato-Sobolev space IN(Lp,κ) by means of |α|=NDαfLp,κ - the sum of the Campanato norms of the derivatives Dαf with |α|=N; the second is to characterize Morrey's fractional integrals {Tf:fLp,κ} in the Campanato-Sobolev space Is(Lp,κ); the third is to find a distributional solution F(Lq,λ)n of the mean curvature type divergence equation divF=fLp,κ (the Morrey space). And yet, the here-established three theorems and their proofs are not only novel but also nontrivial.



中文翻译:

坎帕纳托-索伯列夫空间和div F  =  f中的莫里分数积分

本文的目的是三个方面:首先是确定Campanato-Sobolev空间 一世ñ大号pκ 通过 |α|=ñdαF大号pκ -衍生品的Campanato规范的总和 dαF|α|=ñ; 第二个是刻画Morrey的分数积分{ŤFF大号pκ} 在Campanato-Sobolev空间 一世s大号pκ; 第三是找到分配解决方案F大号qλñ 平均曲率类型散度方程 divF=F大号pκ(莫里空间)。但是,这里建立的三个定理及其证明不仅新颖,而且意义非凡。

更新日期:2020-08-24
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