A critical growth rate for harmonic and subharmonic functions in the open ball in
Krzysztof Samotij (1987)
Colloquium Mathematicae
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Krzysztof Samotij (1987)
Colloquium Mathematicae
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Salvador Pérez-Esteva (1996)
Studia Mathematica
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We study the duals of the spaces of harmonic functions in the unit ball of with values in a Banach space X, belonging to the Bochner space with weight , denoted by . For 0 < α < p-1 we construct continuous projections onto providing a decomposition . We discuss the conditions on p, α and X for which and , 1/p+1/q = 1. The last equality is equivalent to the Radon-Nikodým property of X*.
Stephen M. Buckley, Pekka Koskela (1999)
Commentationes Mathematicae Universitatis Carolinae
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Let be a relatively closed subset of a Euclidean domain . We investigate when solutions to certain elliptic equations on are restrictions of solutions on all of . Specifically, we show that if is not too large, and has a suitable decay rate near , then can be so extended.
V. Anandam, M. Damlakhi (2003)
Annales Polonici Mathematici
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Some properties of the functions of the form in ℝⁿ, n ≥ 2, where each is a harmonic function defined outside a compact set, are obtained using the harmonic measures.
Agnieszka Sibelska (2010)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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The article of J. Clunie and T. Sheil-Small [3], published in 1984, intensified the investigations of complex functions harmonic in the unit disc . In particular, many papers about some classes of complex mappings with the coefficient conditions have been published. Consideration of this type was undertaken in the period 1998–2004 by Y. Avci and E. Złotkiewicz [2], A. Ganczar [5], Z. J. Jakubowski, G. Adamczyk, A. Łazinska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri...
Fanghua Lin, Tristan Rivière (1999)
Journal of the European Mathematical Society
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There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a -valued function defined on the boundary of a bounded regular domain of . When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic map away from a codimension-2 minimal current minimizing the area within...
Jang-Mei Wu (2002)
Studia Mathematica
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Let D be an open set in ℝⁿ (n ≥ 2) and ω(·,D) be the harmonic measure on with respect to the symmetric α-stable process (0 < α < 2) killed upon leaving D. We study inequalities on volumes or capacities which imply that a set S on ∂D has zero harmonic measure and others which imply that S has positive harmonic measure. In general, it is the relative sizes of the sets S and that determine whether ω(S,D) is zero or positive.
Elisabetta Barletta (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Given a Hörmander system on a domain we show that any subelliptic harmonic morphism from into a -dimensional riemannian manifold is a (smooth) subelliptic harmonic map (in the sense of J. Jost & C-J. Xu, [9]). Also is a submersion provided that and has rank . If (the Heisenberg group) and , where is the Lewy operator, then a smooth map is a subelliptic harmonic morphism if and only if is a harmonic morphism, where is the canonical circle bundle and ...
Mustapha Chadli, Mohamed El Kadiri, Sabah Haddad (2005)
Commentationes Mathematicae Universitatis Carolinae
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Let and be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from to is a continuous map from to which preserves the biharmonic structures of and . In the present work we study this notion and characterize in some cases the biharmonic morphisms between and in terms of harmonic morphisms between the harmonic spaces associated with and and the coupling kernels of them.