GuoChun Wen, Yanhui Zhang
LMAM, School of Mathematical Sciences
Peking University
Beijing, 100871, P.R. CHINA
Department of Mathematics
Beijing Technology and Business University
Beijing, 100048, P.R. CHINA

Abstract. In this article, we discuss that the discontinuous oblique derivative boundary value problem for nonlinear uniformly elliptic system of second order equations in multiply connected domains. We first propose the discontinuous oblique derivative problem and its new modified well-posedness. Next we give a priori estimates of solutions of the modified discontinuous boundary value problem for corresponding elliptic system of first order complex equations and verify its solvability by the above estimates of solutions and the Leray-Schauder theorem. Finally the solvability results of the original discontinuous oblique derivative problem can be derived. Here we mention the discontinuous boundary value problems possess many applications in mechanics and physics etc.

Received: October 26, 2013

AMS Subject Classification: 35J57, 35J60, 35B45

Key Words and Phrases: discontinuous oblique derivative problems, elliptic systems of second order equations, estimates and existence of solutions, multiply connected domains

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