(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known datais an armonic function and

fC(^{2}R^{2})

a) Suposse a point P_{0}/f_{xx}(P_{0})> 0. Prove that P_{0}is not a extreme value.

b) consider D = {(x,y) / x^{2}+ y^{2}< 1} and suposse f_{xx}> 0 for all (x,y) in D. Prove that: if f(x,y) = 0 in x^{2}+ y^{2}= 1, so f(x,y) = 0 for all (x,y) in D.

2. Relevant equations

In armonic funcions laplacian = 0

3. The attempt at a solution

I intuit that P_{0}is a saddle point, and I try to show this in the hessian matrix and I can´t

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# Homework Help: Extrems values on armonic function

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