Boundary Value Problems
Volume 2007 (2007), Article ID 24806, 19 pages
Research Article

Harnack Inequality for the Schrödinger Problem Relative to Strongly Local Riemannian p-Homogeneous Forms with a Potential in the Kato Class

Marco Biroli1,2 and Silvana Marchi3

1Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, Piazza Leonardo Da Vinci 32, 20133 Milano, Italy
2Accademia Nazionale delle Scienze detta dei XL, Via L. Spallanzani 7, 00161 Roma, Italy
3Dipartimento di Matematica, Università di Parma, Viale Usberti 53/A, 43100 Parma, Italy

Received 17 May 2006; Revised 14 September 2006; Accepted 21 September 2006

Academic Editor: Ugo Gianazza

Copyright © 2007 Marco Biroli and Silvana Marchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.