Boundary Value Problems (Jan 2007)

Harnack Inequality for the Schr&#246;dinger Problem Relative to Strongly Local Riemannian <inline-formula><graphic file="1687-2770-2007-024806-i1.gif"/></inline-formula>-Homogeneous Forms with a Potential in the Kato Class

  • Marchi Silvana,
  • Biroli Marco

Journal volume & issue
Vol. 2007, no. 1
p. 024806

Abstract

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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.