Displaying similar documents to “Boundary integral methods for harmonic differential forms in 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.

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.

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.

Convex domains and unique continuation at the boundary.

Vilhelm Adolfsson, Luis Escauriaza, Carlos Kenig (1995)

Revista Matemática Iberoamericana

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We show that a harmonic function which vanishes continuously on an open set of the boundary of a convex domain cannot have a normal derivative which vanishes on a subset of positive surface measure. We also prove a similar result for caloric functions vanishing on the lateral boundary of a convex cylinder.