Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

机译：度量标准测量空间中的SoboLev空间：斜率的反射性和较低的半连续性

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In this paper we make a survey of some recent developments of the theory of Sobolev spaces W~(1,q)（X,d,m）, 1 < q < ∞, in metric measure spaces (X, d,m). In the final part of the paper we provide a new proof of the reflexivity of the Sobolev space based on Γ-convergence; this result extends Cheeger's work because no Poincaré inequality is needed and the measure-theoretic doubling property is weakened to the metric doubling property of the support of m. We also discuss the lower semicontinuity of the slope of Lipschitz functions and some open problems.

机译：在本文中，我们对SoboLev Spaces的理论的一些最新进展进行了调查，从而在度量标准度量空间中（x，d，m）中的一个（1，q）（x，d，m），1

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《Conference on Variational Methods for Evolving Objicts》|2015年|294 pages :|共58页
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作者
Luigi Ambrosio; Maria Colombo; Simone Di Marino;
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中图分类 O176-532;
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Sobolev spaces; metric measure spaces; weak gradients;

机译：sobolev spaces;度量标准测量空间;弱梯度;

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1. In Metric-measure Spaces Sobolev Embedding is Equivalent to a Lower Bound for the Measure [J] . Gorka Przemysaw Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis . 2017,第1期

机译：在度量标准空间中，SoboLev嵌入相当于测量的下限
2. The Sharp Sobolev Inequality on Metric Measure Spaces with Lower Ricci Curvature Bounds [J] . Profeta Angelo Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis . 2015,第3期

机译：具有较低Ricci曲率界线的度量度量空间上的Sharp Sobolev不等式
3. Lower Semicontinuity for Parametric Weak Vector Variational Inequalities in Reflexive Banach Spaces [J] . Zhong R.-Y., Huang N.-J. Journal of Optimization Theory and Applications . 2011,第3期

机译：自反Banach空间中参数弱矢量变分不等式的下半连续性
4. Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope [C] . Luigi Ambrosio, Maria Colombo, Simone Di Marino Conference on Variational Methods for Evolving Objicts . 2015

机译：度量标准测量空间中的SoboLev空间：斜率的反射性和较低的半连续性
5. Multidimensional Scaling: Infinite Metric Measure Spaces [D] . Kassab, Lara. 2019

机译：多维缩放：无限度量标准空间
6. THE SEMIGROUP OF METRIC MEASURE SPACES AND ITS INFINITELY DIVISIBLE PROBABILITY MEASURES [O] . STEVEN N. EVANS, ILYA MOLCHANOV -1

机译：度量度量空间的半数及其无限可分的概率度量
7. In Metric-measure Spaces Sobolev Embedding is Equivalent to a Lower Bound for the Measure [O] . Przemysław Górka 2016

机译：在度量空间中，Sobolev嵌入等效于度量的下界

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

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