Hardy inequalities for the Heisenberg Laplacian on convex bounded polytopes

• Bartosch Ruszkowski ^[1]
  1. [1] University of Stuttgart

     University of Stuttgart

     Stadtkreis Stuttgart, Alemania

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 123, Nº 1, 2018, págs. 101-120
• Idioma: inglés
• DOI: 10.7146/math.scand.a-105218
• Texto completo no disponible (Saber más ...)
• Resumen

  • We prove a Hardy-type inequality for the gradient of the Heisenberg Laplacian on open bounded convex polytopes on the first Heisenberg group. The integral weight of the Hardy inequality is given by the distance function to the boundary measured with respect to the Carnot-Carathéodory metric. The constant depends on the number of hyperplanes, given by the boundary of the convex polytope, which are not orthogonal to the hyperplane x3=0.