On the Dirichlet problem for linear elliptic equations in plane domains with corners
A. Azzam (1983)
Annales Polonici Mathematici
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Displaying similar documents to “The computation of capacity of planar condensers.”
On the Dirichlet problem for linear elliptic equations in plane domains with corners
The successive approximation method for the Dirichlet problem in a planar domain
Dagmar Medková (2008)
Applicationes Mathematicae
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The Dirichlet problem for the Laplace equation for a planar domain with piecewise-smooth boundary is studied using the indirect integral equation method. The domain is bounded or unbounded. It is not supposed that the boundary is connected. The boundary conditions are continuous or p-integrable functions. It is proved that a solution of the corresponding integral equation can be obtained using the successive approximation method.
On numerical solution of the Dirichlet problem by the method of locally-canonical decomposition.
Khubezhty, Sh.S. (2003)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Domains of Dirichlet forms and effective resistance estimates on p.c.f. fractals
Jiaxin Hu, Xingsheng Wang (2006)
Studia Mathematica
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We consider post-critically finite self-similar fractals with regular harmonic structures. We first obtain effective resistance estimates in terms of the Euclidean metric, which in particular imply the embedding theorem for the domains of the Dirichlet forms associated with the harmonic structures. We then characterize the domains of the Dirichlet forms.
Connectedness of the Carathéodory discs for doubly connected domains
Leonhard Frerick, Gerald Schmieder (2005)
Annales Polonici Mathematici
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We prove that the Carathéodory discs for doubly connected domains in the complex plane are connected.
On nonisometric isospectral connected fractal domains.
Brian D. Sleeman, Chen Hua (2000)
Revista Matemática Iberoamericana
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A fundamental question raised by M. Kac in 1966 is: Must two isospectral planar domains necessarily be isometric? Following a long history of investigation C. Gordon, D. L. Webb and S. Wolpert in 1992 finally proved that the answer is no. By using the idea of transposition maps one can construct a wide class of planar domains with piecewise continuous boundaries which are isospectral but non-isometric. In this note we study the Kac question in relation to domains with fractal boundaries...
Erratum of “The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent”
Yannick Privat, Mario Sigalotti (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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On Leja-Górski approximations in the spatial Dirichlet's problem
W. Kleiner (1966)
Colloquium Mathematicae
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The product of two Dirichlet series
Frédéric Bayart (2004)
Acta Arithmetica
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Exhaustions of John domains.
Väisälä, Jussi (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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On locally divided integral domains and CPI-overrings.
Dobbs, David E. (1981)
International Journal of Mathematics and Mathematical Sciences
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A note on the fourth moment of Dirichlet L-functions
H. M. Bui, D. R. Heath-Brown (2010)
Acta Arithmetica
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A numerical solution of the Dirichlet problem on some special doubly connected regions
Miroslav Dont, Eva Dontová (1998)
Applications of Mathematics
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The aim of this paper is to give a convergence proof of a numerical method for the Dirichlet problem on doubly connected plane regions using the method of reflection across the exterior boundary curve (which is analytic) combined with integral equations extended over the interior boundary curve (which may be irregular with infinitely many angular points).