Abstract
Equivalence is demonstrated between a generalized form of the inequality of Faber–Krahn and an inequality of Sobolev–Orlicz. Equivalences with estimates on the decay of the heat kernel and inequalities on capacities and Green's functions are also given.
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Carron, G. Inégalités de Faber–Krahn et Inclusion de Sobolev–Orlicz. Potential Analysis 7, 555–575 (1997). https://doi.org/10.1023/A:1017913419876
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DOI: https://doi.org/10.1023/A:1017913419876