微分形式和电流的Sobolev Poincaré不等式

IF 0.2 Q4 MATHEMATICS

Bruno Pini Mathematical Analysis Seminar Pub Date : 2019-12-31 DOI:10.6092/ISSN.2240-2829/10361

A. Baldi

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引用次数: 0

摘要

在本文中，我们收集了在与Franchi和Pansu的联合研究中获得的关于微分形式的（p，q）Poincare和Sobolev不等式的R^n中的一些结果。特别是，我们关注的是p=1的情况。从几何角度来看，微分形式的Poincare和Sobolev不等式提供了上同调消失的定量公式。作为在p＝1的情况下获得的结果的应用，我们获得了欧几里得电流的Poincare和Sobolev不等式。

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Sobolev-Poincaré inequalities for differential forms and currents

In this note we collect some results in R^n about (p,q) Poincare and Sobolev inequalities for differential forms obtained in a joint research with Franchi and Pansu. In particular, we focus to the case p=1. From the geometric point of view, Poincare and Sobolev inequalities for differential forms provide a quantitative formulation of the vanishing of the cohomology. As an application of the results obtained in the case p=1 we obtain Poincare and Sobolev inequalities for Euclidean currents.

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来源期刊

Bruno Pini Mathematical Analysis Seminar MATHEMATICS-

CiteScore

0.30

自引率

0.00%

发文量

审稿时长

15 weeks