MHB Understanding the Harmonic Function Problem

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Please help me I am struggle with this question
Thank you in advance
 
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Well, do you know what a Harmonic Function is?

In this case, to be Harmonic, you would need $\displaystyle \begin{align*} \frac{\partial ^2 u}{\partial x^2} + \frac{\partial ^2 u}{\partial y^2} = 0 \end{align*}$...
 
Prove It said:
Well, do you know what a Harmonic Function is?

In this case, to be Harmonic, you would need $\displaystyle \begin{align*} \frac{\partial ^2 u}{\partial x^2} + \frac{\partial ^2 u}{\partial y^2} = 0 \end{align*}$...
Thank you for helping me
 

Thread '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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