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

Find an expression involving the function [tex]\phi(x_1, x_2, x_3)[/tex] that has a minimum average value of the square of its gradient within a certain volume V of space.

2. Relevant equations

We are studying functionals, though so far it has only been of one variable. We're considering [tex]J[y]=\int_{x_1}^{x_2}f(y, y'; x)dx[/tex] where [tex]y[/tex] is a function of x. This functional is minimized when f satisfies [tex]\frac{\delta f}{\delta y}-\frac{d}{dx}(\frac{\delta f}{\delta y'})=0[/tex]

3. The attempt at a solution

I have no idea how to apply this minimization principle with multiple variables.

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# Homework Help: Minimization of the square of the gradient in a volume

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