- #1

siclar

- 1

- 0

## Homework Statement

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.

## Homework 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]

## The Attempt at a Solution

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