On the paradox of two domains in Schwarzschild exterior solution
A. Zięba (1972)
Colloquium Mathematicae
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A. Zięba (1972)
Colloquium Mathematicae
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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 .
Li Chen, Yujuan Chen, Dang Luo (2013)
Annales Polonici Mathematici
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We study necessary and sufficient conditions for the existence of nonnegative boundary blow-up solutions to the cooperative system in a smooth bounded domain of , where is the p-Laplacian operator defined by with p > 1, f and g are nondecreasing, nonnegative C¹ functions, and α and β are two positive parameters. The asymptotic behavior of solutions near the boundary is obtained and we get a uniqueness result for p = 2.
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 .
Honghui Yin, Zuodong Yang (2012)
Annales Polonici Mathematici
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Our main purpose is to establish the existence of a positive solution of the system ⎧, x ∈ Ω, ⎨, x ∈ Ω, ⎩u = v = 0, x ∈ ∂Ω, where is a bounded domain with C² boundary, , , λ > 0 is a parameter, p(x),q(x) are functions which satisfy some conditions, and is called the p(x)-Laplacian. We give existence results and consider the asymptotic behavior of solutions near the boundary. We do not assume any symmetry conditions on the system.
Nakayashiki, Ryota
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In this paper, we consider a class of initial-boundary value problems for quasilinear PDEs, subject to the dynamic boundary conditions. Each initial-boundary problem is denoted by (S) with a nonnegative constant , and for any , (S) can be regarded as a vectorial transmission system between the quasilinear equation in the spatial domain , and the parabolic equation on the boundary , having a sufficient smoothness. The objective of this study is to establish a mathematical method,...
Per Åhag, Rafał Czyż (2007)
Annales Polonici Mathematici
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Let be a bounded hyperconvex domain in and set , j=1,...,s, s≥ 3. Also let ₙ be the symmetrized polydisc in ℂⁿ, n ≥ 3. We characterize those real-valued continuous functions defined on the boundary of D or ₙ which can be extended to the inside to a pluriharmonic function. As an application a complete characterization of the compliant functions is obtained.
Jill Pipher (1992-1993)
Publications mathématiques et informatique de Rennes
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M. Prizzi, M. Rinaldi, K. P. Rybakowski (2002)
Studia Mathematica
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Consider the family uₜ = Δu + G(u), t > 0, , , t > 0, , of semilinear Neumann boundary value problems, where, for ε > 0 small, the set is a thin domain in , possibly with holes, which collapses, as ε → 0⁺, onto a (curved) k-dimensional submanifold of . If G is dissipative, then equation has a global attractor . We identify a “limit” equation for the family , prove convergence of trajectories and establish an upper semicontinuity result for the family as ε → 0⁺. ...
Svobodová, Ivona
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We consider functionals of a potential energy corresponding to . We are dealing with with . Various types of the subsoil of the plate are described by various types of the nonlinear term . The aim of the paper is to find a suitable computational algorithm.
Kyong T. Hahn, Josephine Mitchell (1973)
Annales Polonici Mathematici
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Stephen J. Gardiner (2014)
Annales de l’institut Fourier
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A holomorphic function on a simply connected domain is said to possess a universal Taylor series about a point in if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta outside (provided only that has connected complement). This paper shows that this property is not conformally invariant, and, in the case where is the unit disc, that such functions have extreme angular boundary behaviour.
Francesca De Marchis, Isabella Ianni, Filomena Pacella (2015)
Journal of the European Mathematical Society
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We consider the semilinear Lane–Emden problem where and is a smooth bounded domain of . The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of , as . Among other results we show, under some symmetry assumptions on , that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as , and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of...
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....
J. Siciak (1985)
Matematički Vesnik
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Anna Grimaldi Piro, Francesco Ragnedda (1991)
Annales Polonici Mathematici
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Abstract. We study a Neumann problem for the heat equation in a cylindrical domain with -base and data in , a subspace of 1. We derive our results, considering the action of an adjoint operator on , a predual of , and using known properties of this last space.
Ruyun Ma (2002)
Annales Polonici Mathematici
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Let α,β,γ,δ ≥ 0 and ϱ:= γβ + αγ + αδ > 0. Let ψ(t) = β + αt, ϕ(t) = γ + δ - γt, t ∈ [0,1]. We study the existence of positive solutions for the m-point boundary value problem ⎧u” + h(t)f(u) = 0, 0 < t < 1, ⎨ ⎩, where , (for i ∈ 1,…,m-2) are given constants satisfying , and . We show the existence of positive solutions if f is either superlinear or sublinear by a simple application of a fixed point theorem in cones. Our result extends a result established by Erbe and...
Rafał Czyż (2009)
Annales Polonici Mathematici
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Let be a bounded hyperconvex domain in and set , j=1,...,s, s ≥ 3. Also let be the image of D under the proper holomorphic map π. We characterize those continuous functions that can be extended to a real-valued pluriharmonic function in .
Pham Hoang Hiep (2007)
Annales Polonici Mathematici
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We study boundary values of functions in Cegrell’s class .