SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR ELLIPTIC SYSTEMS OF SECOND ORDER IN HIGH DIMENSIONAL DOMAINS1

This paper mainly concerns oblique derivative problems for nonlinear non divergent elliptic systems of several second order equations with measurable coefficients in a multiply connected domain. Firstly, we give a priori estimates of solutions for the above boundary value problems with some conditions, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence of solutions for the above problems is proved. Keywords: Oblique derivative problems, nonlinear elliptic systems, high dimensional domain. AMS No: 35J65, 35J55, 35J45.