Hi, can anyone help me prove the following. Suppose that u(x,y) and v(x,y) are smooth functions satisfying the Cauchy-Riemann equations. Prove that v(x,y) is harmonic. thank you
Follow Math Help Forum on Facebook and Google+
Originally Posted by pasleycakes Hi, can anyone help me prove the following. Suppose that u(x,y) and v(x,y) are smooth functions satisfying the Cauchy-Riemann equations. Prove that v(x,y) is harmonic. thank you Yes, but the important question is, "Can you prove it?" The Cauchy-Riemann equations are: (1) (2) . Differentiate (1) with respect to y and (2) with respect to x. Remember that, as long as the second derivatives are continuous, .
Last edited by HallsofIvy; May 31st 2010 at 06:08 AM.
View Tag Cloud