4. Prove that u (x, y) = x³ - 3xy² - x² + y² is harmonic on harmonic conjugate. R². Then find its

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.
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4. Prove that u (x, y) = x³ — 3xy² — x² + y² is harmonic on R². Then find its
harmonic conjugate.
Transcribed Image Text:- 4. Prove that u (x, y) = x³ — 3xy² — x² + y² is harmonic on R². Then find its harmonic conjugate.
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