Classification of well‐posed kinetic layer problems II: The index formula

Abstract

In the kinetic theory of gases, half‐space problems are important because they govern the behavior of correctors to the Hilbert expansion near the boundaries. This paper takes up the discussion in Coron et al., Comm. Pure Appl. Math. 41 (1988) by a different method, based on the index formula for Wiener–Hopf operators on the half‐line. This method leads naturally to a new result on analogues of Chandrasekhar’s $H$ function, which does not seem easy to obtain by the energy method of Coron et al. (1988).