Results 121 to 130 of about 28,148 (143)

Zaremba's problem for elliptic equations in the neighborhood of a singular point or in the infinity

Applicable Analysis, 1998
In the present paper the behavior of solutions of the mixed Zaremba's problem in the neighborhood of a boundary point and at infinity is studied. In part I of this paper[4] the concept of Wiener's generalized solution of Zaremba's problem was introduced and the so called Growth Lemma for the class of domains, satisfying isoperimetric condition, was ...
A.I. Ibragimov, E.M. Landis
openaire   +1 more source

Unique Solvability of the Zaremba Problem for Linear Second Order Elliptic Equations with Drift

Journal of Mathematical Sciences
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Alkhutov, Yu. A., Chechkin, G. A.
openaire   +2 more sources

Bojarski-Meyers estimate for a solution to the Zaremba problem for Poisson's equations with drift

Sbornik: Mathematics
An estimate for the increased integrability is obtained for the gradient of the solution to the Zaremba problem for Poisson's equation with lower-order terms in a bounded domain with Lipschitz boundary and frequent alternation of Dirichlet and Neumann conditions. Bibliography: 22 titles.
Yuriy Alexandrovich Alkhutov, Gregory Aleksandrovich Chechkin   +1 more
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Behavior of the solution of the Zaremba problem near a singular point of the boundary

Mathematical Notes of the Academy of Sciences of the USSR, 1985
Es seien \(G\subset {\mathbb{R}}^ n\), \(n>2\), mit dem Rand \(\Gamma\), \(F\subset \Gamma\) mit positiver Wiener-Kapazität und \({\mathcal L}u:=-\sum (a_{ij}(x)u_{x_ j})_{x_ i}\) ein elliptischer Operator mit reellen meßbaren Koeffizienten. Der Verf. untersucht in der vorliegenden Note das Randverhalten der Lösungen von \({\mathcal L}u=f\) mit \(u| F ...
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On the Solvability of the Zaremba Problem in Infinite Sectors and the Invertibility of Associated Singular Integral Operators

2017
This paper is concerned with the study of invertibility properties of a singular integral operator naturally associated with the Zaremba problem for the Laplacian in infinite sectors in two dimensions, when considering its action on an appropriate Lebesgue scale of p integrable functions, for 1 < p < ∞.
Hussein Awala, Irina Mitrea, Katharine Ott   +2 more
openaire   +1 more source

An Analogue of Schwartz’s Method for the Construction of the Green Function of the Zaremba Problem and Its Application in Underground Hydrodynamics

1998
In the present paper the classical problem of underground hydrodynamics, modeling the flow of incompressible fluid in porous medium, (see e.g. [1,2]) is studied.
A. I. Ibragimov, A. A. Nekrasov
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An analogue of the wiener criterion for the zaremba problem in a cylindrical domain

Functional Analysis and Its Applications, 1983
Kerimov, T. M., Maz'ya, V. G., Novruzov, A. A.   +2 more
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A criterion for the regularity of the point at infinity for the Zaremba problem in a semicylinder

The asymptotic behaviour at infinity of solutions to the Zaremba problem for the Laplace operator in a half-cylinder is studied. Pointwise estimates for solutions, the Green function and the harmonic measure are obtained in terms of the Wiener capacity. The main result is a necessary and sufficient condition for regularity of a point at infinity.
Kerimov, T. M., Maz'ya, V. G., Novruzov, A. A.   +2 more
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On singularities of solutions of a system of integral equations in potential theory for the Zaremba problem

Translation from Vestn. Leningr. Univ. 1983, No.1, Mat. Mekh. Astron. No.1, 43-48 (Russian) (1983; Zbl 0512.31003).
Zargaryan, S. S., Maz'ya, V. G.
openaire   +2 more sources

Numerical Study of the Zaremba Problem

Doklady Mathematics, 2022
exaly