Harnack inequality for harmonic functions relative to a nonlinear -homogeneous Riemannian Dirichlet form

✍ Scribed by Marco Biroli; Paola Vernole

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 189 KB
• Volume: 64
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2005.06.007

✦ Synopsis

We consider a Riemannian (p-homogeneous) Dirichlet functional

(p > 1) defined on D, where D is a dense subspace of L p (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).