# Laplace's EQ, Dirichlet cond, problem at definition

1. Sep 11, 2008

### Somefantastik

$$\Omega = B(0,1) = \left\{ (r,\theta) \in R^{2} : 0 \leq r < 1, -\pi \leq \theta \leq \pi \right\}$$

(problem for the unit disk)

find function $$u(r,\theta)$$ in $$C^{2}(\Omega) \cap C^{0}(\overline{\Omega})$$

such that

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

$$u(1,\theta) = f(\theta); \ \ \\ \ -\pi \leq \theta \leq \pi,$$

Where f is given in $$C^{0}(\partial \Omega)$$

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