Displaying similar documents to “Uniqueness of Dirichlet, Neumann, and mixed boundary value problems for Laplace's and Poisson's equations for a rectangle.”

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.

Some variants of the method of fundamental solutions: regularization using radial and nearly radial basis functions

Csaba Gáspár (2013)

Open Mathematics

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The method of fundamental solutions and some versions applied to mixed boundary value problems are considered. Several strategies are outlined to avoid the problems due to the singularity of the fundamental solutions: the use of higher order fundamental solutions, and the use of nearly fundamental solutions and special fundamental solutions concentrated on lines instead of points. The errors of the approximations as well as the problem of ill-conditioned matrices are illustrated via...

Nonlinear boundary value problems for ordinary differential equations

Andrzej Granas, Ronald Guenther, John Lee

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CommentsThis tract is intended to be accessible to a broad spectrum of readers. Those with out much previous experience with differential equations might find it profitable (when the need arises) to consult one of the following standard texts: Coddington-Levinson [17], Hale [35], Hartman [38], Mawhin-Rouche [61]. The bibliography given below is restricted mostly to the problems discussed in the tract or closely related topics. A small number of additional references are included however...