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2. a) Let u(x, y) be a continous function on a closed and bounded, simply connected region R. Also let u(x, y) be non-constant harmonic function in R. Show that u(x, y) has a maximum value in R which is assumed on the boundary of R and never in the interior.

2. a) Let u(x, y) be a continous function on a closed and bounded, simply connected region R. Also let u(x, y) be non-constant harmonic function in R. Show that u(x, y) has a maximum value in R which is assumed on the boundary of R and never in the interior.

Advanced Engineering Mathematics
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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(it is advanced theory of complex funtion question.)

solve the 1st question in the picture

2. a) Let u(x, y) be a continous function on a closed and bounded, simply connected region R. Also let u(x, y) be non-constant harmonic function in R. Show that u(x, y) has a maximum value in R which is assumed on the boundary of R and never in the interior. b) Find the maximum and minimum values of the function u(x, y) = e' cos x throughout the region {(x, y):0sxs 2n, 0 s ys n}.
Transcribed Image Text:2. a) Let u(x, y) be a continous function on a closed and bounded, simply connected region R. Also let u(x, y) be non-constant harmonic function in R. Show that u(x, y) has a maximum value in R which is assumed on the boundary of R and never in the interior. b) Find the maximum and minimum values of the function u(x, y) = e' cos x throughout the region {(x, y):0sxs 2n, 0 s ys n}.
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