Let $(M,g)$ be a compact smooth Riemannian manifold without boundary, let $(N,h)$ be a smooth Riemannian manifold, and let $u:M\to N$ be a smooth map. Define the Dirichlet energy functional
for smooth maps $v:M\to N$, where $\operatorname{vol}_g$ is the Riemannian volume measure on $M$. Let $\tau(u)\in \Gamma(u^{-1}TN)$ denote the tension field