International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 2, Pages 339-346

Optimal control of nonsmooth system governed by quasi-linear elliptic equations

Gong Liutang and Fei Pusheng

Department of Mathematics, Wuhan University, Wuhan 430072, China

Received 20 June 1995; Revised 20 September 1995

Copyright © 1997 Gong Liutang and Fei Pusheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we discuss a class of optimal control problems of nonsmooth systems governed by quasi-linear elliptic partial differential equations, give the existence of the problem. Through the smoothness and the approximation of the original problem, we get the necessary condition, which can be considered as the Euler-Lagrange condition under quasi-linear case.