$L_\infty$-estimates for the torsion function and $L_\infty$-growth of   semigroups satisfying Gaussian bounds
  We investigate selfadjoint $C_0$-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 $L_\infty$ operator norm of the semigroup. As an application we prove a new $L_\infty$-bound for the torsion function of a Euclidean domain that is close to optimal. 
Hendrik Vogt
math.AP math.FA math.SP