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I am currently learning about boundary value problems and how to calculate their weak formulations. I came across something called "Energy Functional" some call it "The Energy of a System" and I could not find a proper definition for this.

So what is an "Energy Functional"? And what do we need it for? How can we come up with the formula?

Also, if you have good books about this topic, I would be grateful.

Tarek Acila
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  • I am not so sure if there is a good definition. Try replacing the word "Energy" with $L^2$ or $H^1$. – Jacky Chong Mar 19 '22 at 08:16
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    In general, the energy functional is a conserved or dissipative quantity of the system, i.e. it doesn't change with respect to time if you are studying evolutionary system or it gets smaller as time goes by. Either way, the quantity will allow you to have some control over certain norms of the solution. The most common norm that the energy functional could control is the $H^1$ norm of the solution. – Jacky Chong Mar 19 '22 at 08:20

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