Uniqueness of Dirichlet, Neumann, and mixed boundary value problems for Laplace's and Poisson's equations for a rectangle.
J. B. Díaz, R. B. Ram (1979)
Collectanea Mathematica
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J. B. Díaz, R. B. Ram (1979)
Collectanea Mathematica
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Vladimir Ryazanov (2015)
Open Mathematics
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It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.
Dagmar Medková (1998)
Archivum Mathematicum
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Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed.
Nečas, J.
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Dagmar Medková (2003)
Czechoslovak Mathematical Journal
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A necessary and sufficient condition for the continuous extendibility of a solution of the Neumann problem for the Laplace equation is given.
Jan Chabrowski (1982)
Manuscripta mathematica
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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.