This article is part of the series Harnack's Estimates, Positivity and Local Behavior of Degenerate and Singular Parabolic Equations.

Open Access Research Article

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

Marco Biroli1,2* and Silvana Marchi3

Author Affiliations

1 Dipartimento di Matematica "Francesco Brioschi", Politecnico di Milano, Piazza Leonardo Da Vinci 32, 20133 Milano, Italy

2 Accademia Nazionale delle Scienze detta dei XL, Via L. Spallanzani 7, 00161 Roma, Italy

3 Dipartimento di Matematica, Università di Parma, Viale Usberti 53/A, 43100 Parma, Italy

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Boundary Value Problems 2007, 2007:024806 doi:10.1155/2007/24806


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/024806


Received:17 May 2006
Revisions received:14 September 2006
Accepted:21 September 2006
Published:14 February 2007

© 2007 Biroli and 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 -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.

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