2. In this problem we prove that if Au(x, y) bounded function then u must be a constant. Hence if u is harmonic on the whole plane and non-constant then u must approach oo or -o along some direction. = 0 for all points in the x, y plane and u is a (1) Suppose u is bounded in the sense that Ju(x, y)| < M for all (x, y). Show that v(x, y) u(x, y) + M is a harmonic function with v(x, y) 2 0 everywhere.

2. In this problem we prove that if Au(x, y) bounded function then u must be a constant. Hence if u is harmonic on the whole plane and non-constant then u must approach oo or -o along some direction. = 0 for all points in the x, y plane and u is a (1) Suppose u is bounded in the sense that Ju(x, y)| < M for all (x, y). Show that v(x, y) u(x, y) + M is a harmonic function with v(x, y) 2 0 everywhere.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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