On the regularity of weak solutions of quasi-linear elliptic transmission problems on polyhedral domains

The regularity of weak solutions of quasi-linear elliptic boundary transmission problems of p-structure on polyhedral domains Omega is considered. Omega is divided into polyhedral subdomains Omega(i) 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 Omega(i). The proof relies on a difference quotient technique which is based on the ideas of C. Ebmeyer and J. Frehse.