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Annales Polonici Mathematici

1991 | 55 | 1 | 37-56
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $M_pΓ(E₀,E₁,D) = cap_p(E₀,E₁,D)$, where $M_pΓ(E₀,E₁,D)$ is the p-module of the arc family Γ(E₀,E₁,D), while $cap_p(E₀,E₁,D)$ is the p-capacity of E₀,E₁ relative to D and p > 1. One of these cases is when p = n, E̅₀ ∩ E̅₁ = ∅, $E_i = E'_i ∪ E''_i ∪ E'''_i ∪ F_i$, $E'_i$ 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.
Słowa kluczowe
EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
37-56
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-08-15
Twórcy
autor
• Institute of Mathematics, Romanian Academy of Sciences, Iaşi Branch, Bdul Copou 8, Iaşi, Romania
Bibliografia
• [1] P. P. Caraman, p-Capacity and p-modulus, Symposia Math. 18 (1976), 455-484.
• [2] P. P. Caraman, About equality between the p-module and the p-capacity in $ℝ^n$, in: Analytic Functions, Proc. Conf. Błażejewko 1982, Lecture Notes in Math. 1039, Springer, Berlin 1983, 32-83.
• [3] P. P. Caraman, p-module and p-capacity of a topological cylinder, Rev. Roumaine Math. Pures Appl. (1991) (in print).
• [4] P. P. Caraman, p-module and p-capacity in $ℝ^n$, Rev. Roumaine Math. Pures Appl. (in print).
• [5] B. Fuglede, Extremal length and functional completion, Acta Math. 98 (1957), 171-219.
• [6] J. Hesse, Modulus and capacity, Ph.D. Thesis, Univ. of Michigan, Ann Arbor, Michigan, 1972.
• [7] J. Hesse, A p-extremal length and p-capacity equality, Ark. Mat. 13 (1975), 131-144.
• [8] J. Väisälä, On quasiconformal mappings in space, Ann. Acad. Sci. Fenn. Ser. AI Math. 298 (1961), 1-36.
• [9] W. Ziemer, Extremal length and conformal capacity, Trans. Amer. Math. Soc. 126 (1967), 460-473.
• [10] W. Ziemer, Extremal length and p-capacity, Michigan Math. J. 16 (1969), 43-51.
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Bibliografia
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