Korevaar-Schoen-Sobolev spaces and critical exponents in metric measure spaces

被引：4

作者：

Baudoin, Fabrice ^{[1
]}

机构：

[1] Aarhus Univ, Dept Math, Ny Munkegade 118, DK-8000 Aarhus, Denmark

来源：

ANNALES FENNICI MATHEMATICI | 2024年 / 49卷 / 02期

关键词：

Fractals; Sobolev spaces; Korevaar-Schoen space; HEAT KERNELS; POINCARE INEQUALITIES; DIFFUSION-PROCESSES; DIRICHLET FORMS; BROWNIAN-MOTION; P-ENERGY; FRACTALS; PROOF; SETS;

D O I：

10.54330/afm.147513

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We survey, unify and present new developments in the theory of Korevaar-Schoen- Sobolev spaces on metric measure spaces. While this theory coincides with those of Cheeger and Shanmugalingam if the space is doubling and supports a Poincar & eacute; inequality, it offers new perspectives in the context of fractals for which the approach by weak upper gradients is inadequate.

引用

页码：487 / 527

页数：41

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