\begin{abstract} Let $M$ be a complete Riemannian manifold and $G$ Lie subgroup of the isometry group acting freely properly on $M.$ We study Dirichlet Problem% \[ \left\{ \begin{array} [c]{l}% \operatorname{div}\left( \frac{a\left( \left\Vert \nabla u\right\Vert \right) }{\left\Vert }\nabla u\right) =0\text{ in }\Omega u|\partial\Omega=\varphi \end{array} \right. \] where $\Omega$ is $G-$invar...

Lecture 10 on Differential Equations & Differential Invariants introduced equational differential invariants of the form e = 0 for differential equations that are much more general than the ones supported by axiom [′] from Lecture 5 on Dynamical Systems & Dynamic Axioms. Axiom [′] replaces properties of differential equations with universally quantified properties of solutions, but is limited t...