Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted