Dirichlet Problem

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Dirichlet problem

[‚dē·rē′klā ‚präb·ləm]
To determine a solution to Laplace's equation which satisfies certain conditions in a region and on its boundary.

Dirichlet Problem


(named after P. G. L. Dirichlet), the problem of finding a harmonic function from its values given on the boundary of the region under consideration.

References in periodicals archive ?
1) is also known as the modified Dirichlet problem [11, 27, 30] and the Schwarz problem [9, 11].
Numerical solution of the dirichlet problem for elliptic parabolic equations.
GE, Infinitely many positive solutions of a singular Dirichlet problem involving the p-Laplacian, Commun.
From the uniqueness theorem for the exterior Dirichlet problem [5,6] we obtain div [u.
No date is cited for the first edition, but to this second has been added a final chapter on the existence of solutions, primarily the Dirichlet problem for various types of elliptic equations.
Zhang, Existence of solutionas for p(x)-Laplacian Dirichlet problem, Nonlinear Analysis: TMA, 52(2003), 1843-1852.
They cover the Cauchy problem, the Dirichlet problem, the Neumann problem, the Neumann problem for a nonlocal nonlinear diffusion equation, nonlocal p-Laplacian evolution problems, the nonlocal total variation flow, and nonlocal models for sandpiles.
A generalization to Polytopes and a reduction of any Dirichlet problem on compacta is mapped into a unit cube in more dimensions.
We will find that, for the most part, there is a natural homotopy connecting the Neumann modes to those of a corresponding Dirichlet problem (IBC-Dirichlet modes).
We compare the regularizators of a diffraction and a Dirichlet problem, and we prove that the regularizator of a diffraction problem tends to the regularizator of a Dirichlet problem as the parameter of the external domain tends to zero.
If the unknown is prescribed on the boundary of the region, the problem is known as a Dirichlet Problem.
Michael Viscardi's project, entitled On the Solution of the Dirichlet Problem with Rational Boundary Data, develops exciting new approaches to a mathematical problem first formulated in the 19th century by the French mathematician, Lejeune Dirichlet.