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Laplace's EQ, Dirichlet cond, problem at definition

  1. Sep 11, 2008 #1
    [tex] \Omega = B(0,1) = \left\{ (r,\theta) \in R^{2} : 0 \leq r < 1, -\pi \leq \theta \leq \pi \right\} [/tex]

    (problem for the unit disk)

    find function [tex]u(r,\theta) [/tex] in [tex]C^{2}(\Omega) \cap C^{0}(\overline{\Omega}) [/tex]

    such that

    [tex] \nabla^{2}u(r,\theta) = 0; \ \ \ 0 \leq r < 1, \ \ \ \ -\pi \leq \theta \leq \pi, [/tex]

    [tex]u(1,\theta) = f(\theta); \ \ \\ \ -\pi \leq \theta \leq \pi, [/tex]

    Where f is given in [tex] C^{0}(\partial \Omega) [/tex]

    I'm unclear what [tex] C^{0}(\overline{\Omega}) [/tex] and [tex] C^{0}(\partial \Omega) [/tex] exactly means. Can someone help me out with that?

    Thanks in advance!
     
  2. jcsd
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