New cases of equality between p-module and p-capacity

Petru Caraman

Petru Caraman

Annales Polonici Mathematici, Tome 55 (1991), p. 37-56 / Harvested from The Polish Digital Mathematics Library

Résumé

Let E₀, E₁ be two subsets of the closure D̅ of a domain D of the Euclidean n-space $ℝ^{n}$ and Γ(E₀,E₁,D) the family of arcs joining E₀ to E₁ in D. We establish new cases of equality $M_{p} Γ (E ₀, E ₁, D) = c a p_{p} (E ₀, E ₁, D)$ , where $M_{p} Γ (E ₀, E ₁, D)$ is the p-module of the arc family Γ(E₀,E₁,D), while $c a p_{p} (E ₀, E ₁, D)$ is the p-capacity of E₀,E₁ relative to D and p > 1. One of these cases is when p = n, E̅₀ ∩ E̅₁ = ∅, $E_{i} = E_{i}^{'} \cup E_{i}^{''} \cup E_{i}^{'''} \cup F_{i}$ , $E_{i}^{'}$ is inaccessible from D by rectifiable arcs, $E_{i}^{''}$ is open relative to D̅ or to the boundary ∂D of D, $E_{i}^{'''}$ is at most countable, $F_{i}$ is closed (i = 0,1) and D is bounded and m-smooth on (F₀ ∪ F₁) ∩ ∂D.

Publié le : 1991-01-01

Zbl 0748.31003

EUDML-ID : urn:eudml:doc:262233

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     author = {Petru Caraman},
     title = {New cases of equality between p-module and p-capacity},
     journal = {Annales Polonici Mathematici},
     volume = {55},
     year = {1991},
     pages = {37-56},
     zbl = {0748.31003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p37bwm}
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Petru Caraman. New cases of equality between p-module and p-capacity. Annales Polonici Mathematici, Tome 55 (1991) pp. 37-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p37bwm/

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