Harnack inequality for harmonic functions relative to a nonlinear \(p\)-homogeneous Riemannian Dirichlet form (Q5921808)

Consider a Riemannian (\(p\)-homogeneous) Dirichlet functional \[ \Phi(u)=\int_X \mu(u) (dx) \] defined on a dense subspace \(D\) of \(L^p(X,m),\) \(p>1,\) where \(X\) is a locally compact Hausdorff topological space endowed with the distance connected to \(\Phi(u).\) Setting \[ a(u,v)=\int_X \tilde\mu(u,v) (dx) \] for the Dirichlet form related to \(\Phi(u),\) the authors prove a Harnack-type inequality for the positive harmonic functions relative to the form \(a(u,v).\) As a consequence, Hölder continuity is obtained for these functions.