L infinity resolvent bounds for steady Boltzmann's equation

Abstract

We derive lower bounds on the resolvent operator for the linearized steady Boltzmann equation over weighted L1 Banach spaces in velocity, comparable to those derived by Pogan & Zumbrun in an analogous weighted L2 Hilbert space setting. These show in particular that the operator norm of the resolvent kernel is unbounded in Lp(R) for all $1<p \leq \infty$, resolving an apparent discrepancy in behavior between the two settings suggested by previous work.