English

$L_\infty$-estimates for the torsion function and $L_\infty$-growth of semigroups satisfying Gaussian bounds

Analysis of PDEs 2018-05-15 v3 Functional Analysis Spectral Theory

Abstract

We investigate selfadjoint C0C_0-semigroups on Euclidean domains satisfying Gaussian upper bounds. Major examples are semigroups generated by second order uniformly elliptic operators with Kato potentials and magnetic fields. We study the long time behaviour of the LL_\infty operator norm of the semigroup. As an application we prove a new LL_\infty-bound for the torsion function of a Euclidean domain that is close to optimal.

Keywords

Cite

@article{arxiv.1611.03676,
  title  = {$L_\infty$-estimates for the torsion function and $L_\infty$-growth of semigroups satisfying Gaussian bounds},
  author = {Hendrik Vogt},
  journal= {arXiv preprint arXiv:1611.03676},
  year   = {2018}
}