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

DOI10.1515/anona-2023-0119OpenAlexW4391528934WikidataQ128665440 ScholiaQ128665440MaRDI QIDQ6119525

Xiang-Yun Xie, Ji Zheng Huang, Yu Liu, Pengtao Li

Publication date: 1 March 2024

Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/anona-2023-0119

zbMATH Keywords

capacityheat kernelSobolev inequalityDirichlet spaceBV space

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Potential theory on fractals and metric spaces (31E05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Characterizations of sets of finite perimeter using heat kernels in metric spaces
• Regularity of sets with quasiminimal boundary surfaces in metric spaces
• Geometry and analysis of Dirichlet forms. II
• Extensions and traces of functions of bounded variation on metric spaces
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• Fine properties and a notion of quasicontinuity for BV functions on metric spaces
• Perimeter as relaxed Minkowski content in metric measure spaces
• BV capacity on generalized Grushin plane
• Comparisons of relative BV-capacities and Sobolev capacity in metric spaces
• Geometry and analysis of Dirichlet forms
• Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality
• The sharp Sobolev and isoperimetric inequalities split twice
• Functions of bounded variation on ``good metric spaces
• Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces
• Reverse Poincaré inequalities, isoperimetry, and Riesz transforms in Carnot groups
• On gradient bounds for the heat kernel on the Heisenberg group
• The BV-capacity in metric spaces
• Gradient estimates for the subelliptic heat kernel on H-type groups
• Fine properties of sets of finite perimeter in doubling metric measure spaces
• Trace theorems for functions of bounded variation in metric spaces
• Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
• Analysis on local Dirichlet spaces. III: The parabolic Harnack inequality
• Capacities and 1-strict subsets in metric spaces
• Gagliardo-Nirenberg, Trudinger-Moser and Morrey inequalities on Dirichlet spaces
• Flux \& radii within the subconformal capacity
• Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates
• Equivalent definitions of \(BV\) space and of total variation on metric measure spaces
• Restriction of heat equation with Newton-Sobolev data on metric measure space
• Gradient estimates for heat kernels and harmonic functions
• Besov class via heat semigroup on Dirichlet spaces. I: Sobolev type inequalities
• The Li-Yau inequality and heat kernels on metric measure spaces
• Sobolev, Poincaré, and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Differential one-forms on Dirichlet spaces and Bakry-Émery estimates on metric graphs
• Sobolev Spaces on Metric Measure Spaces
• Lebesgue points and capacities via boxing inequality in metric spaces
• Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces