Rearrangement Optimization for Some Elliptic Equations

We investigate an optimization problem related to an elliptic (linear and nonlinear) boundary-value problem. The competing objects are elements of a rearrangement class generated by a fixed positive function. The popular case where the generator is a characteristic function is also considered. In this case, the method of the domain derivative is used to obtain a free boundary result. This research was initiated when the first author was visiting the Iran University of Science and Technology in Summer of 2005. Behrouz Emamizadeh acknowledges the partial financial support from the Petroleum Institute.