JournalsjstVol. 8, No. 4pp. 1295–1348

On the domain of Dirac and Laplace type operators on stratified spaces

  • Luiz Hartmann

    Universidade Federal de São Carlos, Brazil
  • Matthias Lesch

    Universität Bonn, Germany
  • Boris Vertman

    Universität Oldenburg, Germany
On the domain of Dirac and Laplace type operators on stratified spaces cover
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Abstract

We consider a generalized Dirac operator on a compact stratified space with an iterated cone-edge metric. Assuming a spectral Witt condition, we prove its essential self-adjointness and identify its domain and the domain of its square with weighted edge Sobolev spaces. This sharpens previous results where the minimal domain is shown only to be a subset of an intersection of weighted edge Sobolev spaces. Our argument does not rely on microlocal techniques and is very explicit. The novelty of our approach is the use of an abstract functional analytic notion of interpolation scales. Our results hold for the Gauss–Bonnet and spin Dirac operators satisfying a spectral Witt condition.

Cite this article

Luiz Hartmann, Matthias Lesch, Boris Vertman, On the domain of Dirac and Laplace type operators on stratified spaces. J. Spectr. Theory 8 (2018), no. 4, pp. 1295–1348

DOI 10.4171/JST/228