### Dirichlet problems for distribution boundary values

H. J. Bremermann (1967)

Colloquium Mathematicae

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H. J. Bremermann (1967)

Colloquium Mathematicae

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Ali I. Abdul-Latif (1978)

Collectanea 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.

I. Babuska, Manil Suri (1987)

Numerische Mathematik

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Mohsen Khaleghi Moghadam, Johnny Henderson (2017)

Open Mathematics

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Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p(k)-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Ricceri-local minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.

Martin Schechter (1992)

Annales Polonici Mathematici

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We show that one can drop an important hypothesis of the saddle point theorem without affecting the result. We then show how this leads to stronger results in applications.

J.-L. Doob (1957)

Séminaire Brelot-Choquet-Deny. Théorie du potentiel

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Filippo Cammaroto, Francesca Faraci (2012)

Annales Polonici Mathematici

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We deal with some Dirichlet problems involving a nonlocal term. The existence of two nonzero, nonnegative solutions is achieved by applying a recent result by Ricceri.

John W. Barrett, Charles M. Elliott (1986)

Numerische Mathematik

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Nečas, J.

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R. Kreß, W.T. Spassov (1983)

Numerische Mathematik

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Currie, Sonja, Love, Anne D. (2010)

Advances in Difference Equations [electronic only]

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Faker Ben Belgacem, Henda El Fekih, Hejer Metoui (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for...