Quasiadditivity of Capacity and Minimal Thinness
نویسنده
چکیده
It is well known that a capacity C is countably subadditive, i.e. We shall prove that the reverse inequality, up to a multiplicative constant, holds for some decomposition of E , provided there is a measure comparable to C. Such a property will be referred to as quasiadditivity. As an application, we shall show that the Green energy for a uniformly-regular domain is quasiadditive with respect to the Whitney decomposition of the domain. The Hardy inequality due to Ancona 3, (1)] will be a main tool. We shall apply the quasiadditivity of the Green energy to obtain a reened Wiener criterion for minimal thinness in an NTA domain.
منابع مشابه
Quasiadditivity of Riesz Capacity
holds with some positive constant N . We refer to this inequality as “quasiadditivity”. Quasiadditivity for decompositions into spherical shells has been considered by Landkof [9, Lemma 5.5 in p.304] and Adams [1, Theorem 7.5]. In the case of Green energy (for the definition see Section 5), quasiadditivity for the Whitney decomposition (cf. [14, p.16]) of a half space is discussed in Essén [5]....
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