JournalsjstVol. 6 , No. 4pp. 903–919

Heat kernel estimates for general boundary problems

  • Liangpan Li

    Loughborough University, UK
  • Alexander Strohmaier

    Loughborough University, UK
Heat kernel estimates for general boundary problems cover
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Abstract

We show that not feeling the boundary estimates for heat kernels hold for any non-negative self-adjoint extension of the Laplace operator acting on vector-valued compactly supported functions on a domain in Rd\mathbb R^d . They are therefore valid for any choice of boundary condition and we show that the implied constants can be chosen independent of the self-adjoint extension. The method of proof is very general and is based on finite propagation speed estimates and explicit Fourier Tauberian theorems obtained by Y. Safarov.

Cite this article

Liangpan Li, Alexander Strohmaier, Heat kernel estimates for general boundary problems. J. Spectr. Theory 6 (2016), no. 4 pp. 903–919

DOI 10.4171/JST/147