Abstract:
Integral equations for the Dirichlet problem for the Laplace operator are studied in a plane domain whose boundary has interior or exterior peaks with tangency of first order. Theorems on unique solvability and asymptotics of solutions near the peaks are presented.
Bibliography: 8 titles.
Citation:
V. G. Maz'ya, A. A. Soloviev, “On an integral equation for the Dirichlet problem in a plane domain with cusps on the boundary”, Math. USSR-Sb., 68:1 (1991), 61–83
\Bibitem{MazSol89}
\by V.~G.~Maz'ya, A.~A.~Soloviev
\paper On an integral equation for the Dirichlet problem in a~plane domain with cusps on the boundary
\jour Math. USSR-Sb.
\yr 1991
\vol 68
\issue 1
\pages 61--83
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Linking options:
https://www.mathnet.ru/eng/sm1657
https://doi.org/10.1070/SM1991v068n01ABEH001196
https://www.mathnet.ru/eng/sm/v180/i9/p1211
This publication is cited in the following 8 articles:
Bezrodnykh S. Bogatyrev A. Goreinov S. Grigor'ev O. Hakula H. Vuorinen M., “On Capacity Computation For Symmetric Polygonal Condensers”, J. Comput. Appl. Math., 361 (2019), 271–282
Hyeonbae Kang, Hyundae Lee, KiHyun Yun, “Optimal estimates and asymptotics for the stress concentration between closely located stiff inclusions”, Math. Ann, 2015
Mazya V.G., Poborchii S.V., “O predstavlenii resheniya zadachi Neimana v oblasti s pikom garmonicheskim potentsialom prostogo sloya”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 1: Matem., Mekh., Astronom., 2009, no. 3, 41–49
Mazya V.G., Poborchii S.V., “Odnoznachnaya razreshimost integralnogo uravneniya dlya garmonicheskogo potentsiala prostogo sloya na granitse oblasti s pikom”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 1: Matem., Mekh., Astronom., 2009, no. 2, 63–73
Kokilashvili V. Meshveliani Z. Paatashvili V., “Boundary Value Problems for Analytic and Harmonic Functions of Smirnov Classes in Domains with Non-Smooth Boundaries”, Factorization, Singular Operators and Related Problems, Proceedings, ed. Samko S. Lebre A. DosSantos A., Springer, 2003, 175–196
Chkadua O., “The Dirichlet, Neumann and Mixed Boundary Value Problems of the Theory of Elasticity in N-Dimensional Domains with Boundaries Containing Closed Cuspidal Edges”, Math. Nachr., 189 (1998), 61–105
A. A. Soloviev, “Integral equations for the Dirichlet and Neumann boundary value problems in a plane domain with a cusp on the boundary”, Math. Notes, 59:6 (1996), 637–645
R. Duduchava, T. Latsabidze, A. Saginashvili, “Singular integral operators with the complex conjugation on curves with cusps”, Integr equ oper theory, 22:1 (1995), 1
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