Displaying similar documents to “Note on infinity-superharmonic functions.”

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.

Maximum principle for viscosity sub solutions and viscosity sub solutions of the Laplacian

Sundararaja Ramaswamy (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The aim of this paper is to characterize the u.s.c. (resp. l.s.c.) viscosity sub (resp. super) solutions of the Laplacian which do not take the value + ∞ (resp. - ∞ ) as precisely the sub (resp. super) harmonic functions.

On the existence of weighted boundary limits of harmonic functions

Yoshihiro Mizuta (1990)

Annales de l'institut Fourier

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We study the existence of tangential boundary limits for harmonic functions in a Lipschitz domain, which belong to Orlicz-Sobolev classes. The exceptional sets appearing in this discussion are evaluated by use of Bessel-type capacities as well as Hausdorff measures.

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.