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6.9 Dirichlet Problem for the Upper Half-Plane

6.9 Dirichlet Problem for the Upper Half-Plane. Consider the following problem:. We solved this problem by Fourier Transform :. Goal. We will solve this problem again by Fourier Integral :. 6.9 Dirichlet Problem for the Upper Half-Plane. Goal. Consider the following problem:.

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6.9 Dirichlet Problem for the Upper Half-Plane

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  1. 6.9 Dirichlet Problem for the Upper Half-Plane Consider the following problem: We solved this problem by Fourier Transform: Goal We will solve this problem again by Fourier Integral:

  2. 6.9 Dirichlet Problem for the Upper Half-Plane Goal Consider the following problem: We will solve this problem again by Fourier Integral: We looking for a bounded solution. The Fourier Integral representation of f Fourier integral coefficients of f

  3. 6.9 Dirichlet Problem for the Upper Half-Plane Consider the following problem:

  4. 6.9 Dirichlet Problem for the Upper Half-Plane Consider the following problem: To satisfy the boundary condition we must generally superimpose these conditions over all w >= 0. this is done by integration Fourier Integral expansion of f Boundary condition

  5. 6.9 Dirichlet Problem for the Upper Half-Plane Fourier Integral expansion of f Consider the following problem:

  6. 6.9 Dirichlet Problem for the Upper Half-Plane Ex5/p279 In each Problem obtain the solution of the Dirichlet problem for the upper half-plane, using the given f(x).

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