The differential equation for the extremal of I(u)=iintD[ux^2+uy^2]dx,dy, where u is prescribed on the boundary of D, is:

Q61Section II (Mathematics)61 of 145

The Dirichlet integral leads to Laplace's equation

The differential equation for the extremal of $I(u)=\iint_D\bigl[u_x^2+u_y^2\bigr]dx\,dy$ , where $u$ is prescribed on the boundary of D, is:

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