On the Regularity of Weak Solutions of Quasi-Linear Elliptic Transmission Problems on Polyhedral Domains

Abstract

The regularity of weak solutions of quasi-linear elliptic boundary transmission problems of p-structure on polyhedral domains Ω is considered. Ω is divided into polyhedral subdomains Ωi and it is assumed that the growth properties of the differential operator vary from subdomain to subdomain. We prove higher regularity of weak solutions up to the transmission surfaces, provided that the differential operators are distributed quasi-monotonely with respect to the subdomains Ωi. The proof relies on a difference quotient technique which is based on the ideas of C. Ebmeyer and J. Frehse.