Displaying similar documents to “Distribution function inequalities for the density of the area integral”

Checkerboards, Lipschitz functions and uniform rectifiability.

Peter W. Jones, Nets Hawk Katz, Ana Vargas (1997)

Revista Matemática Iberoamericana

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In his recent lecture at the International Congress [S], Stephen Semmes stated the following conjecture for which we provide a proof. Theorem. Suppose Ω is a bounded open set in Rn with n > 2, and suppose that B(0,1) ⊂ Ω, Hn-1(∂Ω) = M < ∞ (depending on n and M) and a Lipschitz graph Γ (with constant L) such that Hn-1(Γ ∩ ∂Ω) ≥ ε. Here H...

Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains

Jang-Mei G. Wu (1978)

Annales de l'institut Fourier

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On a Lipschitz domain D in R n , three theorems on harmonic functions are proved. The first (boundary Harnack principle) compares two positive harmonic functions at interior points near an open subset of the boundary where both functions vanish. The second extends some familiar geometric facts about the Poisson kernel on a sphere to the Poisson kernel on D . The third theorem, on non-tangential limits of quotient of two positive harmonic functions in D , generalizes Doob’s relative Fatou...

On pseudospheres that are quasispheres.

John L. Lewis, Andrew Vogel (2001)

Revista Matemática Iberoamericana

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We construct bounded domains D not equal to a ball in n ≥ 3 dimensional Euclidean space, R, for which ∂D is homeomorphic to a sphere under a quasiconformal mapping of R and such that n - 1 dimensional Hausdorff measure equals harmonic measure on ∂D.

A note on the Rellich formula in Lipschitz domains.

Alano Ancona (1998)

Publicacions Matemàtiques

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Let L be a symmetric second order uniformly elliptic operator in divergence form acting in a bounded Lipschitz domain ­Ω of R and having Lipschitz coefficients in Ω­. It is shown that the Rellich formula with respect to Ω­ and L extends to all functions in the domain D = {u ∈ H (Ω­); L(u) ∈ L(­Ω)} of L. This answers a question of A. Chaïra and G. Lebeau.