Mathematical Control and Related Fields (MCRF)

Cesari-type conditions for semilinear elliptic equation with leading term containing controls

Pages: 41 - 59, Volume 1, Issue 1, March 2011      doi:10.3934/mcrf.2011.1.41

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Bo Li - School of Mathematical Sciences, Fudan University, Shanghai 200433, China (email)
Hongwei Lou - School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433, China (email)

Abstract: An optimal control problem governed by semilinear elliptic partial differential equation is considered. The equation is in divergence form with the leading term containing controls. By studying the $G$-closure of the leading term, an existence result is established under a Cesari-type condition.

Keywords:  Optimal control, existence condition, elliptic equation, homogenization, Cesari-type condition.
Mathematics Subject Classification:  Primary: 49J20; Secondary: 35B27, 35B37, 35J20.

Received: November 2010;      Revised: February 2011;      Available Online: March 2011.