Explore BrainMass
Share

Partial Differential Equations : Harmonic Function and Constant Function

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

Suppose U is a positive harmonic function which is defined everywhere in the plane. Show that U must be a constant function.

This is a question regarding Poisson Integral Formula in PDE. I need to find it using the Harnak's inequalities.

© BrainMass Inc. brainmass.com October 24, 2018, 9:25 pm ad1c9bdddf
https://brainmass.com/math/partial-differential-equations/partial-differential-equations-harmonic-constant-function-126558

Solution Summary

A harmonic function is shown to be a constant function. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

$2.19
See Also This Related BrainMass Solution

The Laplace Equation in Cylindrical Coordinates

Please see the attached file for a question taken from the "Classical Electrodynamic 3rd by Jackson".

View Full Posting Details