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Dirichlet problem
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(Definition)
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Suppose $\Omega$ is a domain of $\sR^n$ and $\partial\Omega$ is the boundary of $\Omega$ . Further suppose $f$ is a function $f\colon\partial \Omega\to\sC$ . Then the Dirichlet problem is to find a function $\phi\colon \Omega\cup \partial \Omega \to\sC$ such that \begin{eqnarray*} \phi &=& f,\quad \text{on $\partial \Omega$}, \\ \nabla^2 \phi &=& 0,\quad \text{in $\Omega$}. \end{eqnarray*}
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"Dirichlet problem" is owned by matte. [ full author list (2) ]
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Cross-references: function, boundary, domain
There are 5 references to this entry.
This is version 4 of Dirichlet problem, born on 2005-01-16, modified 2005-06-07.
Object id is 6646, canonical name is DirichletProblem.
Accessed 7970 times total.
Classification:
| AMS MSC: | 31A05 (Potential theory :: Two-dimensional theory :: Harmonic, subharmonic, superharmonic functions) | | | 31B05 (Potential theory :: Higher-dimensional theory :: Harmonic, subharmonic, superharmonic functions) | | | 31B15 (Potential theory :: Higher-dimensional theory :: Potentials and capacities, extremal length) |
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Pending Errata and Addenda
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