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

Boundary Value Problems volume 2007, Article number: 024806 (2007) Cite this article

Abstract

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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Authors and Affiliations

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

    Marco Biroli

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

    Marco Biroli

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

    Silvana Marchi

Authors
  1. Marco Biroli
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  2. Silvana Marchi
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Correspondence to Marco Biroli.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Biroli, M., Marchi, S. Harnack Inequality for the Schrödinger Problem Relative to Strongly Local Riemannian -Homogeneous Forms with a Potential in the Kato Class. Bound Value Probl 2007, 024806 (2007). https://doi.org/10.1155/2007/24806

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