Boundary behaviour of positive harmonic functions on Lipschitz domains.
Carroll, Tom (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Displaying similar documents to “Convex domains and unique continuation at the boundary.”
Boundary behaviour of positive harmonic functions on Lipschitz domains.
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 -domains
Björn Dahlbert (1979)
Studia 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 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 -nontangential limits. (iii) The localized version of the above two results and nontangential limits of Green potentials under a certain nontangential condition.
Superharmonic functions on Lipschitz domain
Martin Silverstein, Richard Wheeden (1971)
Studia Mathematica
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Oblique derivative problems for the laplacian in Lipschitz domains.
Jill Pipher (1987)
Revista Matemática Iberoamericana
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The aim of this paper is to extend the results of Calderón [1] and Kenig-Pipher [12] on solutions to the oblique derivative problem to the case where the data is assumed to be BMO or Hölder continuous.
Boundary integral methods for harmonic differential forms in Lipschitz domains.
Mitrea, Dorina, Mitrea, Marius (1996)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Fatou theorems for some nonlinear elliptic equations.
Eugene Fabes, Nicola Garofalo, Santiago Marin Malave, Sandro Salsa (1988)
Revista Matemática Iberoamericana
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A remark on gradients of harmonic functions.
Wen Sheng Wang (1995)
Revista Matemática Iberoamericana
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In any C domain, there is nonzero harmonic function C continuous up to the boundary such that the function and its gradient on the boundary vanish on a set of positive measure.
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 in , 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 . The third theorem, on non-tangential limits of quotient of two positive harmonic functions in , generalizes Doob’s relative Fatou...