The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces

The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces

In this article, we consider the bounded variation capacity (BV capacity) and characterize the Sobolev-type inequalities related to BV functions in a general framework of strictly local Dirichlet spaces with a doubling measure via the BV capacity. Under a weak Bakry-Émery curvature-type condition, w...

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Bibliographic Details
Main Authors: Xie Xiangyun, Liu Yu, Li Pengtao, Huang Jizheng
Format: Article
Language:English
Published: De Gruyter 2024-02-01
Series:Advances in Nonlinear Analysis
Subjects:
bv space
dirichlet space
heat kernel
capacity
sobolev inequality
28a12
31e05
26b30
Online Access:https://doi.org/10.1515/anona-2023-0119

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