HARNACK INEQUALITY FOR HARMONIC FUNCTIONS RELATIVE TO A NONLINEAR P-HOMOGENEOUS DIRICHLET FORM

We consider a Riemannian (p-homogeneous) Dirichlet functional?(u)= ?X?(u)(dx)(p>1) defined on D, where D is a dense subspace of Lp(X,m) and X is a locally compact Hausdorff topological space endowed with the distance d connected with ?(u) (see Section 2 for the definitions). We denote by a(u,v)=?X??(u,v)(dx) the Dirichlet form related to ?(u). We prove a Harnack type inequality for positive harmonic function relative to the form a(u,v); as a consequence we obtain also the Hölder continuity of harmonic function relative to the form a(u,v). © 2005 Elsevier Ltd. All rights reserved.