On the boundary domains of the n-th eigenfunctions for the self-adjoined elliptic equation
Jan Bochenek (1965)
Annales Polonici Mathematici
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Jan Bochenek (1965)
Annales Polonici Mathematici
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Mitsuhiro T. Nakao, N. Yamamoto (1993)
Numerische Mathematik
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Maurizio Chicco (2009)
Bollettino dell'Unione Matematica Italiana
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In this note I extend some previuos results concerning a generalized maximum principle for linear second order elliptic equations in divergence form, to the case of unbounded domains.
Przemysław Górka (2007)
Colloquium Mathematicae
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We examine an elliptic equation in a domain Ω whose boundary ∂Ω is countably (m-1)-rectifiable. We also assume that ∂Ω satisfies a geometrical condition. We are interested in an overdetermined boundary value problem (examined by Serrin [Arch. Ration. Mech. Anal. 43 (1971)] for classical solutions on domains with smooth boundary). We show that existence of a solution of this problem implies that Ω is an m-dimensional Euclidean ball.
Sergey V. Lototsky, Boris L. Rozovskii, Xiaoliang Wan (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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This paper discusses analytical and numerical issues related to elliptic equations with random coefficients which are generally nonlinear functions of white noise. Singularity issues are avoided by using the Itô-Skorohod calculus to interpret the interactions between the coefficients and the solution. The solution is constructed by means of the Wiener Chaos (Cameron-Martin) expansions. The existence and uniqueness of the solutions are established under rather weak assumptions, the main...
Xiangxing Tao (2002)
Studia Mathematica
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Let u be a solution to a second order elliptic equation with singular magnetic fields, vanishing continuously on an open subset Γ of the boundary of a Lipschitz domain. An elementary proof of the doubling property for u² over balls centered at some points near Γ is presented. Moreover, we get the unique continuation at the boundary of Dini domains for elliptic operators.
G.R. Burton (1985)
Mathematische Zeitschrift
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Mikhail Borsuk, Krzysztof Żyjewski (2011)
Applicationes Mathematicae
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We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of a boundary corner point. We find an exponent of the solution's decreasing rate under minimal assumptions on the problem coefficients.
Damian Wiśniewski (2016)
Annales Mathematicae Silesianae
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We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.
Fischer, Cyril, Náprstek, Jiří
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The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplification, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect...
Helmut Harbrecht, Jingzhi Li (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this paper, we propose a numerical method to solve stochastic elliptic interface problems with random interfaces. Shape calculus is first employed to derive the shape-Taylor expansion in the framework of the asymptotic perturbation approach. Given the mean field and the two-point correlation function of the random interface, we can thus quantify the mean field and the variance of the random solution in terms of certain orders of the perturbation amplitude by solving a deterministic...
Antoni L. Dawidowicz, Krystyna Twardowska (1988)
Rendiconti del Seminario Matematico della Università di Padova
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