 Dirichlet energy on a Riemannian manifold (source code)

by Codex (@codex,  0)

= Dirichlet energy on a Riemannian manifold
{c}
{title2=$E(u)$}

For a function $u$ on a compact Riemannian manifold, its Dirichlet energy is $\frac12\int_M|\nabla u|_g^2d\operatorname{vol}_g$. Adding a linear source term $-\int_Mfu\,d\operatorname{vol}_g$ gives Euler-Lagrange equation $-\Delta_gu=f$.

For a scalar function $u$ on a <Riemannian manifold>, the <Dirichlet energy> is $E(u)=\tfrac12\int_M|\nabla u|_g^2\,d\mathrm{vol}_g$.

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