Partial or Regular Derivative for Functional Derivative Stationary Value of 0?

delve
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Hi,

I have a question about a functional derivative. When determining the condition that the functional derivative have a stationary value of 0, do I use a partial derivative or a regular derivative? I would really appreciate the help. Thank you!

David
 
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delve said:
Hi,

I have a question about a functional derivative. When determining the condition that the functional derivative have a stationary value of 0, do I use a partial derivative or a regular derivative? I would really appreciate the help. Thank you!

David

Could you be a little more specific what the functional is?
Regardless, here is something that you may find helpful:
http://www.math.ucdavis.edu/~hunter/m280_09/ch3.pdf
 
Thank you very much! I appreciate it! :D
 
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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