The \(\infty \)-capacity and Faber-Krahn inequality on Grushin spaces

DOI10.1007/s00605-021-01557-1zbMath1471.32060OpenAlexW3159069662MaRDI QIDQ2049540

Yu Liu, Guo-liang Li

Publication date: 27 August 2021

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-021-01557-1

zbMATH Keywords

capacityCarnot-Carathéodory spaceGrushin spaces

Mathematics Subject Classification ID

Sub-Riemannian geometry (53C17) Capacity theory and generalizations (32U20)

Cites Work

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• Isoperimetric problem in \(H\)-type groups and Grushin spaces
• Lipschitz extensions on generalized Grushin spaces
• The BV-capacity in metric spaces
• Besov capacity and Hausdorff measures in metric measure spaces
• Properties of infinite harmonic functions on Grushin-type spaces
• Differentiability of Lipschitz functions on metric measure spaces
• Functional capacities on the Grushin space \({\mathbb {G}}^n_\alpha \)
• Relative \(\infty\)-capacity and its affinization
• Isoperimetric inequality in the Grushin plane
• The \(\infty\)-eigenvalue problem
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Viscosity solutions on Grushin-type planes
• Capacities in metric spaces
• Bilipschitz Embedding of Grushin Plane in R^3
• Sharp capacitary estimates for rings in metric spaces
• The Fundamental Solution to the p-Laplacian in a class of H\"ormander Vector Fields
• The 𝑃-Laplace equation on a class of Grushin-type spaces
• Geometric PDEs in the Grushin Plane: Weighted Inequalities and Flatness of Level Sets
• User’s guide to viscosity solutions of second order partial differential equations
• Sobolev met Poincaré
• Sobolev Spaces on Metric Measure Spaces
• Lebesgue points and capacities via boxing inequality in metric spaces
• [https://portal.mardi4nfdi.de/wiki/Publication:5689214 Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces]
• Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations
• Optimal Lipschitz extensions and the infinity Laplacian
• Surface measures in Carnot-Carathéodory spaces