1. The problem statement, all variables and given/known data Note: path-connected means arcwise-connected C^0 means continuous ⊿f=Laplacian=(f)xx+(f)yy df/dn = grad f ． n 2. Relevant material Green's theorem, line integrals, ... 3. The attempt at a solution The only part I can finish is part (ii): (ii) follows from the vector version of Green's theorem by letting F=grad f How can I do parts (i) and (iii)? And provided that I have proved (i), (ii), and (iii), how would these results aid me in proving the actual problem? Any help or hints would be greatly appreciated!