Canonical mappings in
Z. Abdul-Hadi, D. Bschouty, W. Hengartner (1985)
Matematički Vesnik
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Z. Abdul-Hadi, D. Bschouty, W. Hengartner (1985)
Matematički Vesnik
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Marek Jarnicki, Peter Pflug (1997)
Annales Polonici Mathematici
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We present various characterizations of n-circled domains of holomorphy with respect to some subspaces of .
J. Siciak (1985)
Matematički Vesnik
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A. Zięba (1972)
Colloquium Mathematicae
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Wojciech M. Zajączkowski
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CONTENTS1. Introduction.......................................................................52. Notation and auxiliary results............................................93. Statement of the problem (1.1)-(1.3)..............................204. The problem (3.14).........................................................225. Auxiliary results in ...............................................346. Existence of solutions of (3.14) in ............417. Green function................................................................528....
M. Sango (2003)
Colloquium Mathematicae
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We study the initial boundary value problem for the system of thermoelasticity in a sequence of perforated cylindrical domains , s = 1,2,... We prove that as s → ∞, the solution of the problem converges in appropriate topologies to the solution of a limit initial boundary value problem of the same type but containing some additional terms which are expressed in terms of quantities related to the geometry of . We give an explicit construction of that limit problem.
Kyong T. Hahn, Josephine Mitchell (1973)
Annales Polonici Mathematici
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Edgar Lee Stout (2006)
Annales Polonici Mathematici
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We construct a domain of holomorphy in , N≥ 2, whose envelope of holomorphy is not diffeomorphic to a domain in .
Alessandro Perotti (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Viene studiata l'equazione per le forme regolari sulla chiusura dell'intersezione di domini pseudoconvessi. Si costruisce un operatore soluzione in forma integrale e sotto ipotesi opportune si ottengono stime della soluzione nelle norme .
A. Aytuna, A. Rashkovskii, V. Zahariuta (2002)
Annales Polonici Mathematici
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For complete Reinhardt pairs “compact set - domain” K ⊂ D in ℂⁿ, we prove Zahariuta’s conjecture about the exact asymptotics , s → ∞, for the Kolmogorov widths of the compact set in C(K) consisting of all analytic functions in D with moduli not exceeding 1 in D, τ(K,D) being the condenser pluricapacity of K with respect to D.
Yongxiang Li, Huanhuan Zhang (2016)
Annales Polonici Mathematici
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We discuss the existence of positive radial solutions of the semilinear elliptic equation ⎧-Δu = K(|x|)f(u), x ∈ Ω ⎨αu + β ∂u/∂n = 0, x ∈ ∂Ω, ⎩, where , N ≥ 3, K: [r₀,∞) → ℝ⁺ is continuous and , f ∈ C(ℝ⁺,ℝ⁺), f(0) = 0. Under the conditions related to the asymptotic behaviour of f(u)/u at 0 and infinity, the existence of positive radial solutions is obtained. Our conditions are more precise and weaker than the superlinear or sublinear growth conditions. Our discussion is based on the...
Caroline Sweezy (2007)
Annales Polonici Mathematici
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Let L be a strictly elliptic second order operator on a bounded domain Ω ⊂ ℝⁿ. Let u be a solution to in Ω, u = 0 on ∂Ω. Sufficient conditions on two measures, μ and ν defined on Ω, are established which imply that the norm of |∇u| is dominated by the norms of and . If we replace |∇u| by a local Hölder norm of u, the conditions on μ and ν can be significantly weaker.
M. Prizzi, K. P. Rybakowski (2003)
Studia Mathematica
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We study a family of semilinear reaction-diffusion equations on spatial domains , ε > 0, in lying close to a k-dimensional submanifold ℳ of . As ε → 0⁺, the domains collapse onto (a subset of) ℳ. As proved in [15], the above family has a limit equation, which is an abstract semilinear parabolic equation defined on a certain limit phase space denoted by . The definition of , given in the above paper, is very abstract. One of the objectives of this paper is to give more manageable...
Christer O. Kiselman (2015)
Banach Center Publications
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A bounded open set with boundary of class C¹ which is locally weakly lineally convex is weakly lineally convex, but, as shown by Yuriĭ Zelinskiĭ, this is not true for unbounded domains. The purpose here is to construct explicit examples, Hartogs domains, showing this. Their boundary can have regularity or . Obstructions to constructing smoothly bounded domains with certain homogeneity properties will be discussed.
Caroline Sweezy, J. Michael Wilson
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We prove sufficiency of conditions on pairs of measures μ and ν, defined respectively on the interior and the boundary of a bounded Lipschitz domain Ω in d-dimensional Euclidean space, which ensure that, if u is the solution of the Dirichlet problem. Δu = 0 in Ω, , with f belonging to a reasonable test class, then , where 1 < p ≤ q < ∞ and q ≥ 2. Our sufficiency conditions resemble those found by Wheeden and Wilson for the Dirichlet problem on . As in that case we attack the...
Sara Monsurrò, Maria Transirico (2015)
Mathematica Bohemica
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In this review article we present an overview on some a priori estimates in , , recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two -bounds, , for...
Jill Pipher (1992-1993)
Publications mathématiques et informatique de Rennes
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Mohamed Mourad Lhannafi Ait Yahia, Hamid Haddadou (2021)
Applications of Mathematics
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The goal of this paper is to establish a general homogenization result for linearized elasticity of an eigenvalue problem defined over perforated domains, beyond the periodic setting, within the framework of the -convergence theory. Our main homogenization result states that the knowledge of the fourth-order tensor , the -limit of , is sufficient to determine the homogenized eigenvalue problem and preserve the structure of the spectrum. This theorem is proved essentially by using...
El Houssine Azroul, Abdelkrim Barbara, Meryem El Lekhlifi, Mohamed Rhoudaf (2012)
Applicationes Mathematicae
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We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem in Ω, where Ω is a bounded open domain of , N ≥ 2 and is a Carathéodory function satisfying the natural growth condition and the coercivity condition, but with only a weak monotonicity condition. The right hand side f lies in L¹(Ω) and F belongs to .
Lin Wei, Zuodong Yang (2010)
Annales Polonici Mathematici
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We study the existence of positive solutions to ⎧ on Ω, ⎨ ⎩ u = 0 on ∂Ω, where Ω is or an unbounded domain, q(x) is locally Hölder continuous on Ω and p > 1, γ > -(p-1).
Qin Li, Zuodong Yang (2015)
Annales Polonici Mathematici
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By a sub-super solution argument, we study the existence of positive solutions for the system ⎧ in Ω, ⎪ in Ω, ⎨u,v > 0 in Ω, ⎩u = v = 0 on ∂Ω, where Ω is a bounded domain in with smooth boundary or . A nonexistence result is obtained for radially symmetric solutions.
Peter Pflug, Włodzimierz Zwonek (2002)
Studia Mathematica
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We give a characterization of -domains of holomorphy with the help of the boundary behavior of the Bergman kernel and geometric properties of the boundary, respectively.