Harnack Inequality for the Schrödinger Problem Relative to Strongly Local Riemannian http://static-content.springer.com/image/art%3A10.1155%2F2007%2F24806/MediaObjects/13661_2006_Article_639_IEq1_HTML.gif -Homogeneous Forms with a Potential in the Kato Class

  • Marco Biroli1, 2Email author and

    Affiliated with

    • Silvana Marchi3

      Affiliated with

      Boundary Value Problems20072007:024806

      DOI: 10.1155/2007/24806

      Received: 17 May 2006

      Accepted: 21 September 2006

      Published: 14 February 2007

      Abstract

      We define a notion of Kato class of measures relative to a Riemannian strongly local http://static-content.springer.com/image/art%3A10.1155%2F2007%2F24806/MediaObjects/13661_2006_Article_639_IEq2_HTML.gif -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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      Authors’ Affiliations

      (1)
      Dipartimento di Matematica "Francesco Brioschi", Politecnico di Milano
      (2)
      Accademia Nazionale delle Scienze detta dei XL
      (3)
      Dipartimento di Matematica, Università di Parma

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      Copyright

      © M. Biroli and S. Marchi 2007

      This article is published under license to BioMed Central Ltd. 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.