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Elliptic Problems on Unbounded Domains
SIAM Journal on Mathematical Analysis, 1986Boundary value problems for elliptic equations of the form \(\sum_{| \alpha |,| \beta | \leq k}(-1)^{| \alpha |}D^{\alpha}(a_{\alpha \beta}D_ u^{\beta})=f\) on unbounded domains \(\Omega \subset {\mathbb{R}}^ n\) are studied. Using weighted Sobolev spaces, variants of the Poincaré and Friedrichs inequalities, and compact embeddings in weighted Sobolev ...
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The Martin Kernel for Unbounded Domains
Potential Analysis, 2009Let \((x_{1},\widetilde{x})\) denote a typical point of \(\mathbb{R}\times \mathbb{R}^{d-1}\), where \(d\geq 3\), and let \(a:[0,\infty )\rightarrow (0,\infty )\) be Lipschitz. This paper is concerned with unbounded domains \(D\) of the form \(\{(x_{1},\widetilde{x}):x_{1}>0,\;\left| \widetilde{x}\right|
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Approximating Unbounded Domains
2016This chapter provides the construction and approximation of two approaches for the treatment of unbounded domains: first by absorbing boundary conditions (ABC), then by perfectly matched layers (PML) for the three wave equations.
Gary Cohen, Sébastien Pernet
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On the Euler Equation in an Unbounded Domain of the Plane
Journal of Mathematical Fluid Mechanics, 2008We discuss existence and uniqueness of solutions to the Euler Equation in an unbounded domain of the plane. We only assume the vorticity to be bounded, whereas in this kind of problems assumptions on its decreasing at infinity are usually made. The solution is obtained as limit of solutions to problems with compactly supported data.
S. Caprino, MARCHIORO, Carlo
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On defining functions and cores for unbounded domains I
Mathematische Zeitschrift, 2016Abstract We extend the authors’ results on existence of global defining functions to a number of different settings. In particular, we relax the assumption on strict pseudoconvexity of the domain to strict
Tobias Harz +2 more
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On Some Elliptic Problems in Unbounded Domains
Chinese Annals of Mathematics, Series B, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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BRANCHING DIFFUSION PROCESSES IN AN UNBOUNDED DOMAIN
Mathematics of the USSR-Sbornik, 1982In this paper sufficient conditions are found for existence of maximal isolated eigenvalues in the spectrum of the mathematical expectation of a branching diffusion process in an unbounded domain, and limit theorems are proved.Bibliography: 12 titles.
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2002
Although the physical world is finite, from a mathematical point of view, very large domains must often be modeled as infinite ones. This is particularly true for waves which can be propagated on distances which correspond to several hundreds or even several thousands of wavelengths.
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Although the physical world is finite, from a mathematical point of view, very large domains must often be modeled as infinite ones. This is particularly true for waves which can be propagated on distances which correspond to several hundreds or even several thousands of wavelengths.
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Gaugeability for Unbounded Domains
1990Let D be a Greenian domain in R d(d ≥ 1), namely, its Green function G D(x, y) < ∞ for x, y ∈ D, x ≠ y, and let q ∈ K d (see [1] for definition); if q is only given in D, then we assume q(x) = 0 for x ∈ R d — D.
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Symmetric Stable Processes on Unbounded Domains
Potential Analysis, 2006The author gives necessary and sufficient conditions for the expectation of a function of the exit time by a symmetric \(\alpha\)-stable process from a horn-shaped domain to be finite. The results of this paper are generalizations of earlier results contained in a paper by \textit{T. Kulczycki} and the author [Trans. Am. Math. Soc. 358, No.
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