The logarithmic Sobolev capacity

[1]  M. Novaga,et al.  Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature , 2015, Journal für die reine und angewandte Mathematik (Crelles Journal).

[2]  D. Adams.  Choquet integrals in potential theory , 1998 .

[3]  Haim Brezis,et al.  A note on limiting cases of sobolev embeddings and convolution inequalities , 1980 .

[4]  D. Adams.  A note on choquet integrals with respect to Hausdorff capacity , 1988 .

[5]  Gaoyong Zhang,et al.  Sharp convex Lorentz–Sobolev inequalities , 2011 .

[6]  D. Edmunds,et al.  Embeddings in Spaces of Lipschitz Type, Entropy and Approximation Numbers, and Applications , 2000 .

[7]  Characterizations to the fractional Sobolev inequality , 2013, 1312.3135.

[8]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[9]  Zhijian Wu.  Strong type estimate and Carleson measures for Lipschitz spaces , 1999 .

[10]  Eduardo Gonzalez,et al.  The mean curvature of a set of finite perimeter , 1987 .

[11]  F. Cobos,et al.  Embeddings of Besov spaces of logarithmic smoothness , 2014 .

[12]  S. Bianchini.  On Bressan's conjecture on mixing properties of vector fields , 2006 .

[13]  M. Warma,et al.  A class of quasi-linear parabolic and elliptic equations with nonlocal Robin boundary conditions , 2010 .

[14]  W. Burnside.  Theory of Functions , 1899, Nature.

[15]  Mahamadi Warma,et al.  The Fractional Relative Capacity and the Fractional Laplacian with Neumann and Robin Boundary Conditions on Open Sets , 2015 .

[16]  Fernando Cobos,et al.  Approximation spaces, limiting interpolation and Besov spaces , 2015, J. Approx. Theory.

[17]  L. Evans.  Measure theory and fine properties of functions , 1992 .

[18]  Quoc-Hung Nguyen,et al.  On the Sobolev space of functions with derivative of logarithmic order , 2018, Advances in Nonlinear Analysis.

[19]  António M. Caetano,et al.  Sharp embeddings of Besov spaces involving only logarithmic smoothness , 2008, J. Approx. Theory.

[20]  Hans-Gerd Leopold.  Embeddings and entropy numbers in Besov spaces of generalized smoothness , 2000 .

[21]  E. Valdinoci,et al.  Hitchhiker's guide to the fractional Sobolev spaces , 2011, 1104.4345.

[22]  William P. Ziemer,et al.  Integral Inequalities of Poincare and Wirtinger Type for BV Functions , 1977 .

[23]  J. Heinonen,et al.  Nonlinear Potential Theory of Degenerate Elliptic Equations , 1993 .

[24]  L. Hedberg,et al.  Function Spaces and Potential Theory , 1995 .

[25]  Alessio Figalli,et al.  Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies , 2014, Communications in Mathematical Physics.

[26]  H. Triebel,et al.  Spectral theory for isotropic fractal drums , 1998 .

[27]  G. A. Kaljabin.  CHARACTERIZATION OF SPACES OF GENERALIZED LIOUVILLE DIFFERENTIATION , 1977 .

[28]  Timothy S. Murphy,et al.  Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals , 1993 .

[29]  F. Maggi.  Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory , 2012 .

[30]  Y. Netrusov.  Estimates of capacities associated with Besov spaces , 1996 .

[31]  O. Savin,et al.  Nonlocal minimal surfaces , 2009, 0905.1183.

[32]  Enrico Valdinoci,et al.  On the evolution by fractional mean curvature , 2015, Communications in Analysis and Geometry.

[33]  S. Tikhonov,et al.  Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations , 2018, Memoirs of the American Mathematical Society.

[34]  H. Triebel.  Theory Of Function Spaces , 1983 .

[35]  M. Milman,et al.  Extrapolation: Stories and Problems , 2020, 2004.03655.

[36]  D. Edmunds,et al.  Spaces of Lipschitz type, embeddings and entropy numbers , 1999 .

[37]  U. Massari,et al.  Variational mean curvatures in abstract measure spaces , 2016 .

[38]  D. Haroske.  On More General Lipschitz Spaces , 2000 .

[39]  Quoc-Hung Nguyen,et al.  Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields , 2018, Analysis & PDE.

[40]  W. Ziemer.  Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation , 1989 .

[41]  António M. Caetano,et al.  Embeddings and the growth envelope of Besov spaces involving only slowly varying smoothness , 2011, J. Approx. Theory.

[42]  E. Stein,et al.  Real Analysis: Measure Theory, Integration, and Hilbert Spaces , 2005 .

[43]  L. Grafakos.  Classical Fourier Analysis , 2010 .

[44]  D. Adams,et al.  Strong type estimates for homogeneous Besov capacities , 2003 .

[45]  H. Triebel,et al.  Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups , 2016 .

[46]  G. Choquet.  Theory of capacities , 1954 .

[47]  W. Yuan,et al.  A note on dyadic Hausdorff capacities , 2008 .

[48]  M. Fall,et al.  Curves and surfaces with constant nonlocal mean curvature: Meeting Alexandrov and Delaunay , 2015, Journal für die reine und angewandte Mathematik (Crelles Journal).

[49]  Sergey V. Astashkin,et al.  Limiting interpolation spaces via extrapolation , 2018, J. Approx. Theory.

[50]  Fernando Cobos,et al.  Description of logarithmic interpolation spaces by means of the J-functional and applications , 2015 .

[51]  J. Xiao.  Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation , 2006 .

[52]  Gwenael Mercier,et al.  Convergence of Level Sets in Total Variation Denoising Through Variational Curvatures in Unbounded Domains , 2020, SIAM J. Math. Anal..

[53]  Hans-Gerd Leopold,et al.  Characterisations of function spaces of generalised smoothness , 2006 .

[54]  F. Cobos,et al.  On Besov spaces of logarithmic smoothness and Lipschitz spaces , 2015 .

[55]  D. Adams,et al.  Besov functions and vanishing exponential integrability , 2003 .

[56]  P. Lions,et al.  Ordinary differential equations, transport theory and Sobolev spaces , 1989 .

[57]  Björn Jawerth,et al.  Extrapolation theory with applications , 1991 .

[58]  Thierry Gallouët,et al.  Nonlinear Schrödinger evolution equations , 1980 .

[59]  S. Shi,et al.  Fractional capacities relative to bounded open Lipschitz sets complemented , 2017 .

[60]  S. Shi,et al.  On Fractional Capacities Relative to Bounded Open Lipschitz Sets , 2016 .

[61]  Ordinary differential equations and quasiconformal mappings , 1976 .

[62]  Umberto Massari,et al.  Esistenza e regolarità delle ipersuperfici di curvatura media assegnata in Rn , 1974 .