Difference between revisions of "Dirichlet boundary conditions"
From Encyclopedia of Mathematics
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''Dirichlet conditions, Dirichlet data, boundary conditions of the first kind'' | ''Dirichlet conditions, Dirichlet data, boundary conditions of the first kind'' | ||
| − | Consider a second-order partial differential equation | + | Consider a second-order partial differential equation $Lu=f$ on a domain $D$ in $\mathbf R^n$ with boundary $S$ (cf. also [[Differential equation, partial, of the second order|Differential equation, partial, of the second order]]). Boundary conditions of the form |
| − | + | $$u(x)=\phi(x),\quad x\in S,$$ | |
are called Dirichlet boundary conditions. | are called Dirichlet boundary conditions. | ||
Latest revision as of 14:55, 16 October 2014
Dirichlet conditions, Dirichlet data, boundary conditions of the first kind
Consider a second-order partial differential equation $Lu=f$ on a domain $D$ in $\mathbf R^n$ with boundary $S$ (cf. also Differential equation, partial, of the second order). Boundary conditions of the form
$$u(x)=\phi(x),\quad x\in S,$$
are called Dirichlet boundary conditions.
A boundary value problem with Dirichlet conditions is also called a boundary value problem of the first kind (see First boundary value problem).
See also Second boundary value problem; Neumann boundary conditions; Third boundary value problem.
How to Cite This Entry:
Dirichlet boundary conditions. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dirichlet_boundary_conditions&oldid=33678
Dirichlet boundary conditions. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dirichlet_boundary_conditions&oldid=33678
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article