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

100%

Caraman P.

Annales Polonici Mathematici

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1991

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tom 55

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nr 1

37-56

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.

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About a conjecture of F. W. Gehring on the boundary correspondence by quasi-conformal mappings

63%

Caraman P.

Annales Polonici Mathematici

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1976-1977

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tom 33

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nr 1

21-33

3

Boundary behaviour of quasiconformal mappings in normed spaces

51%

Caraman P.

Annales Polonici Mathematici

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1985

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tom 46

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nr 1

35-54

Ograniczanie wyników

3 Annales Polonici Mathematici

3 Caraman P.

1 1991

1 1985

1 1976

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

About a conjecture of F. W. Gehring on the boundary correspondence by quasi-conformal mappings

Boundary behaviour of quasiconformal mappings in normed spaces