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We consider the energy of the torsion problem with Robin boundary conditionsin the case where the solution is not a minimizer. Its dependence on the volumeof the domain and the surface area of the boundary is discussed. In contrast tothe case of positive elasticity constants, the ball does not provide a minimum.For nearly spherical domains and elasticity constants close to zero the energyis largest for the ball. This result is true for general domains in the planeunder an additional condition on the first non-trivial Steklov eigenvalue. Formore general elasticity constants the situation is more involved and it isstrongly related to the particular domain perturbation. The methods used inthis paper are the series representation of the solution in terms of Stekloveigenfunctions, the first and second shape derivatives and an isoperimetricinequality of Payne and Weinberger \cite{PaWe61} for the torsional rigidity.

Domain perturbations for elliptic problems with Robin boundary conditions of opposite sign