On the Schrödinger heat kernel in horn-shaped domains

Tom 99 / 2004

Gabriele Grillo Colloquium Mathematicum 99 (2004), 145-155 MSC: Primary 58J35; Secondary 35B40, 35B05, 47D06. DOI: 10.4064/cm99-2-1

Streszczenie

We prove pointwise lower bounds for the heat kernel of Schrödinger semigroups on Euclidean domains under Dirichlet boundary conditions. The bounds take into account non-Gaussian corrections for the kernel due to the geometry of the domain. The results are applied to prove a general lower bound for the Schrödinger heat kernel in horn-shaped domains without assuming intrinsic ultracontractivity for the free heat semigroup.

Autorzy

  • Gabriele GrilloDipartimento di Matematica
    Politecnico di Torino
    Corso Duca degli Abruzzi 24
    10129 Torino, Italy
    e-mail

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