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• W3201573802 abstract "This paper presents various functional-geometric aspects of the logarithmic Sobolev capacity Caplog⁡,γ,p - a capacity generated by the logarithmic Sobolev space Wplog⁡,γ, where (γ,p)∈(0,∞)×[1,∞). This new nonlinear-inhomogeneous-nontrivial capacity is closely related to the logarithmic Hausdorff capacity. Not only continuously sharp embedding property of Wplog⁡,γ into certain logarithmic weighted Lebesgue space and the tracing inequalities are established, but also the logarithmic perimeter and the Lebesgue measure are utilized to: reformulate Caplog⁡,γ,p; find the first variation of the logarithmic perimeter via the corresponding logarithmic mean curvature; characterize the hypersurface of a constant logarithmic mean curvature." @default.
• W3201573802 created "2021-09-27" @default.
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• W3201573802 date "2021-12-01" @default.
• W3201573802 modified "2023-09-30" @default.
• W3201573802 title "The logarithmic Sobolev capacity" @default.
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• W3201573802 doi "https://doi.org/10.1016/j.aim.2021.107993" @default.
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