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

Jang-Mei G. Wu

Displaying similar documents to “Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains”

The Dirichlet problem for the biharmonic equation in a Lipschitz domain

Björn E. J. Dahlberg, C. E. Kenig, G. C. Verchota (1986)

Annales de l'institut Fourier

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In this paper we study and give optimal estimates for the Dirichlet problem for the biharmonic operator $Δ^{2}$ , on an arbitrary bounded Lipschitz domain $D$ in $R^{n}$ . We establish existence and uniqueness results when the boundary values have first derivatives in $L^{2} (\partial D)$ , and the normal derivative is in $L^{2} (\partial D)$ . The resulting solution $u$ takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of $\nabla u$ is shown to be in $L^{2} (\partial D)$ .

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.

On the Poisson integral for Lipschitz and $C^{1}$ -domains

Björn Dahlbert (1979)

Studia Mathematica

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On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold

John C. Taylor (1978)

Annales de l'institut Fourier

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The Martin compactification of a bounded Lipschitz domain $D \subset R^{n}$ is shown to be $\overline{D}$ for a large class of uniformly elliptic second order partial differential operators on $D$ . Let $X$ be an open Riemannian manifold and let $M \subset X$ be open relatively compact, connected, with Lipschitz boundary. Then $\overline{M}$ is the Martin compactification of $M$ associated with the restriction to $M$ of the Laplace-Beltrami operator on $X$ . Consequently an open Riemannian manifold $X$ has at most one compactification which...

Boundary behaviour of positive harmonic functions on Lipschitz domains.

Carroll, Tom (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

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Boundary behavior of subharmonic functions in nontangential accessible domains

Shiying Zhao (1994)

Studia Mathematica

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The following results concerning boundary behavior of subharmonic functions in the unit ball of $ℝ^{n}$ are generalized to nontangential accessible domains in the sense of Jerison and Kenig [7]: (i) The classical theorem of Littlewood on the radial limits. (ii) Ziomek’s theorem on the $L^{p}$ -nontangential limits. (iii) The localized version of the above two results and nontangential limits of Green potentials under a certain nontangential condition.

Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains

Carlos E. Kenig (1983-1984)

Séminaire Équations aux dérivées partielles (Polytechnique)

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Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains

John L. Lewis, Kaj Nyström (2007)

Annales scientifiques de l'École Normale Supérieure

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