Boundary Value Problems
Volume 2007 (2007), Article ID 24806, 19 pages
doi:10.1155/2007/24806
Harnack Inequality for the Schrödinger Problem Relative to Strongly Local Riemannian p-Homogeneous Forms with a Potential in the Kato Class
Marco Biroli1
and Silvana Marchi2
1Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, Piazza Leonardo Da Vinci 32, 20133 Milano, Italy
2Dipartimento di Matematica, Università di Parma, Viale Usberti 53/A, 43100 Parma, Italy
Abstract
We define a notion of Kato class of measures relative to a Riemannian strongly local p-homogeneous Dirichlet form and we prove a Harnack inequality (on balls that are small enough) for the positive solutions to a Schrödinger-type problem relative to the form with a potential in the Kato class.