Explore BrainMass

Explore BrainMass

    Liouville's theorem

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Suppose that f(z) = u(x , y) + i*v(x, y) (where z = x + i*y) is ENTIRE and not constant. Use Liouville's theorem to prove that v(x, y) is unbounded. Under what conditions can a function that is harmonic everywhere be bounded?

    © BrainMass Inc. brainmass.com October 10, 2019, 12:10 am ad1c9bdddf

    Solution Preview

    Let . Since is entire, then is also entire.
    I claim that is unbounded.
    If is bounded, ...

    Solution Summary

    Liouville's theorem is applied.