Displaying similar documents to “Boundary value problems in domains with peaks.”

On the connectedness of boundary and complement for domains

Andrzej Czarnecki, Marcin Kulczycki, Wojciech Lubawski (2011)

Annales Polonici Mathematici

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This article gives a short and elementary proof of the fact that the connectedness of the boundary of an open domain in ℝⁿ is equivalent to the connectedness of its complement.

Diffusion and propagation problems in some ramified domains with a fractal boundary

Yves Achdou, Christophe Sabot, Nicoletta Tchou (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of ℝ 2 with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized Neumann boundary condition is imposed on the fractal boundary. Sobolev spaces on this domain are studied. In particular, extension and trace results are obtained. These results enable the investigation of the variational formulation of the above mentioned boundary value problems. Next, for...

On the boundary values of harmonic functions.

Paul R. Garabedian (1985)

Revista Matemática Iberoamericana

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Over the years many methods have been discovered to prove the existence of a solution of the Dirichlet problem for Laplace's equation. A fairly recent collection of proofs is based on representations of the Green's functions in terms of the Bergman kernel function or some equivalent linear operator [3]. Perhaps the most fundamental of these approaches involves the projection of an arbitrary function onto the class of harmonic functions in a Hilbert space whose norm is defined by the...

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 propagation of boundary continuity of holomorphic functions of several variables

Salla Franzén, Burglind Jöricke (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove that continuity properties of bounded analytic functions in bounded smoothly bounded pseudoconvex domains in two-dimensional affine space are determined by their behaviour near the Shilov boundary. Namely, if the function has continuous extension to an open subset of the boundary containing the Shilov boundary it extends continuously to the whole boundary. If it is Hölder continuous on such a boundary set, it is Hölder continuous on the closure of the domain. The statements...