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 ?
He discusses in detail the Dirichlet problems for quasilinear and fully nonlinear elliptic equations of the second order: quasilinear uniformly elliptic equations in arbitrary domains, mean curvature equations in domains with non-negative boundary mean curvature, fully nonlinear uniformly elliptic equations in arbitrary domains, and Monge-Ampere equation in uniformly convex domains.
N, and then performs the following two-step iteration: at each iteration k, one first solves Dirichlet problems on each [[OMEGA].
Two kinds of Dirichlet problems are usually considered for biharmonic equation (1).
Papageorgiou, Dirichlet problems with an indefinite and unbounded potential and concave-convex nonlinearities, Abstr.
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
Neuberger, A Reduction Algorithm for Sublinear Dirichlet Problems, Nonlinear Analysis, 47 (2001), 33793390.
Profile graphs of the values for relative elapsed time changes [Delta]T for the mixed and Neumann problems with respect to the Dirichlet problems, [Delta][T.
Passaseo, Nonlinear elliptic Dirichlet problems in exterior domains: the role of geometry and topology of the do-main, Comm.