The logarithmic Sobolev capacity

DOI10.1016/j.aim.2021.107993zbMath1477.31023OpenAlexW3201573802MaRDI QIDQ2237387

Jie Xiao, Li Guang Liu, Wen Yuan, Suqing Wu

Publication date: 27 October 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2021.107993

zbMATH Keywords

logarithmic Hausdorff capacitylogarithmic Sobolev capacitylogarithmic Sobolev space

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (4)

Besov capacity for a class of nonlocal hypoelliptic operators and its applications ⋮ Extension of Q‐type spaces related with weight functions via convolution operators on Heisenberg groups ⋮ Toward weighted Lorentz-Sobolev capacities from Caffarelli-Silvestre extensions ⋮ Differentiability of logarithmic Besov functions in terms of capacities

Cites Work

• Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups
• On fractional capacities relative to bounded open Lipschitz sets
• Hitchhiker's guide to the fractional Sobolev spaces
• Approximation spaces, limiting interpolation and Besov spaces
• On Besov spaces of logarithmic smoothness and Lipschitz spaces
• Variational mean curvatures in abstract measure spaces
• Fractional capacities relative to bounded open Lipschitz sets complemented
• Sharp convex Lorentz-Sobolev inequalities
• Limiting interpolation spaces via extrapolation
• Embeddings and the growth envelope of Besov spaces involving only slowly varying smoothness
• Gaussian capacity analysis
• Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation
• Ordinary differential equations, transport theory and Sobolev spaces
• Strong \(A_{\infty}\)-weights and scaling invariant Besov capacities
• Sharp embeddings of Besov spaces involving only logarithmic smoothness
• A note on dyadic Hausdorff capacities
• Esistenza e regolarita delle ipersuperfici di curvatura media assegnata in \(R^n\)
• Ordinary differential equations and quasiconformal mappings
• Choquet integrals in potential theory
• Estimates of capacities associated with Besov spaces
• Strong type estimates for homogeneous Besov capacities
• Besov functions and vanishing exponential integrability
• Embeddings in spaces of Lipschitz type, entropy and approximation numbers, and applications
• Elliptic partial differential equations of second order
• Curves and surfaces with constant nonlocal mean curvature: meeting Alexandrov and Delaunay
• Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature
• On the Sobolev space of functions with derivative of logarithmic order
• Isoperimetry and stability properties of balls with respect to nonlocal energies
• Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields
• The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets
• Description of logarithmic interpolation spaces by means of the \(J\)-functional and applications
• Characterisations of function spaces of generalised smoothness
• On the evolution by fractional mean curvature
• A class of quasi-linear parabolic and elliptic equations with nonlocal Robin boundary conditions
• Theory of capacities
• Sets of Finite Perimeter and Geometric Variational Problems
• Embeddings of Besov spaces of logarithmic smoothness
• The mean curvature of a set of finite perimeter
• Integral Inequalities of Poincare and Wirtinger Type for BV Functions
• Extrapolation theory with applications
• Classical Fourier Analysis
• Nonlocal minimal surfaces
• A note on limiting cases of sobolev embeddings and convolution inequalities
• Nonlinear Schrödinger evolution equations
• Weakly Differentiable Functions
• CHARACTERIZATION OF SPACES OF GENERALIZED LIOUVILLE DIFFERENTIATION
• Spectral theory for isotropic fractal drums
• Strong type estimate and Carleson measures for Lipschitz spaces
• Characterizations to the fractional Sobolev inequality
• Extrapolation: Stories and Problems
• Uniqueness theorems for surfaces in the large. I, II, III, IV, V
• Sobolev Spaces
• Convergence of Level Sets in Total Variation Denoising Through Variational Curvatures in Unbounded Domains
• On more general Lipschitz spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The logarithmic Sobolev capacity