Question

Determine if this function is harmonic, then determine the largest region B where
This is harmonic:
g(x,y) = ln (x^2 + y^2)

Answer 1

http://www.wolframalpha.com/input/?i=D%5BLog%5Bx%5E2+%2B+y%5E2%5D%2C+%7Bx%2C+2%7D%5D+%2B+D%5BLog%5Bx%5E2+%2B+y%5E2%5D%2C+%7By%2C+2%7D%5D

seems that the function is harmonic on \( \Bbb R^2 \setminus \{(0,0)\} \), \( \log (x^2 + y^2) \) has singularity at \((0,0)\)