| 1. | These are equivalent boundary value problems, and both yield the solution
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| 2. | If so, then we know what our boundary value is.
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| 3. | Each boundary has a valid boundary and an invalid boundary value.
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| 4. | Specifying the boundary conditions, the boundary value problem is completely defined.
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| 5. | It is essential to consider boundary values of Sobolev functions.
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| 6. | Therefore, the final approximate solution to this boundary value problem is,
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| 7. | There are many numerical methods to solve boundary value problems.
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| 8. | Fourier series are used to solve boundary value problems in partial differential equations.
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| 9. | Solutions of boundary value problems for the Laplace equation satisfy the Dirichlet principle.
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| 10. | A large class of important boundary value problems are the Sturm Liouville problems.
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