Recent content by krakatoa

I pretend to use the ecuation twice, once for the interior and another for the vaccum, so if I use the cilindrical coordinates for \nabla_t^2 it results in two Bessel equations, one for the interior and another fot the vaccum. In the vaccum, the fields should experiment a exponential decay, in...

Great, you really help me, the eigenvalues have diferent sign, and it means that is a undefinited cuadratic form, so, is a saddle point, its okey? and about the b) part, if f(x,y)=0, how fxx > 0 ? thanks!

The trace IS the laplacian operator, and is equal to zero, and if the trace is equal to zero so H have not eigenvalues... if H have not eigenvalues, what can i said about the saddle point?

I usually use the sylvester´s criterion (or see the eigenvalues from the hessian matrix) so I try to use this automatically, I thought it would be more simple. The problem is from a curse that not uses linear algebra knowledge. sorry my english is not good.

and why evaluate on zero? if i can see that fxx = - fyy implies that is a saddle point I can do the second part... sory I am confused

With the hessian i can classify the critical points, and i know that fxx > 0 and fyy < 0 (because f is an armonic function)

Homework Statement f[/B] is an armonic function and C2(R2) a) Suposse a point P0 / fxx(P0) > 0. Prove that P0 is not a extreme value. b) consider D = {(x,y) / x2 + y2 < 1} and suposse fxx > 0 for all (x,y) in D. Prove that: if f(x,y) = 0 in x2 + y2 = 1, so f(x,y) = 0 for all (x,y) in D...