The method of deriving the sufficient condition in a domain optimization problem is given.. this method is based on the consideration of symmetry, namely, we take only the shape of domains into account and do not take the place of the domains on the plane into consideration. E apply this method to the two- parameter family of domain optimization problems where the objec- tive functions have quadratic and linear parts. For these problems we give the sufficient conditions and show when the unit circle is the solution of the optimization problem.
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