Dirichlet Problem

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Dirichlet problem

[‚dē·rē′klā ‚präb·ləm]
(mathematics)
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 ?
u] corresponds to solving local symmetric CRFE Dirichlet problems, and the solutions are unique.
kl] u corresponds to solving local nonsymmetric CRVFE Dirichlet problems, the solutions of which are unique.
The Dirichlet problems for higher-order linear differential equations in multiply connected domains have not been solved yet.
The existence of solutions of p(x)-Laplacian Dirichlet problems has been studied in many papers (see e.
There are many papers devoted to the Dirichlet problems of quasilinear elliptic equations, see for example [1], [2], [3].
2005, A numerical method to find a positive solution of semilinear elliptic Dirichlet problems, Applied Mathematics and Computation, Article in Press.
Evaluation of The Di_erence Between The Regularizators of Di_raction and of Dirichlet Problems
Other methods can be pursued similarly to manage the rank deficiency of fully Dirichlet problems.
In this paper, the existence of at least three weak solutions for Dirichlet problems involving the p-Laplacian is established.
We note that these Dirichlet problems are always well posed and that [S.
We observe that, near the vertices, this refinement coincides with the ones introduced in [3, 12, 17, 70] for the Dirichlet problem.
In this article, we discuss the numerical solution of the Dirichlet problem for the real elliptic Monge-Ampere equation, in two dimensions, by an augmented Lagrangian based iterative method.