  Based on the domain variational point of view, we carry on stability analysis
on two shape optimization problems from thermal insulation background. The
novelty is that, we do not require that the second variation is normal to the
boundary. For example, translation variation is not normal, but as one can see
in our work, it not only plays a role in obtaining the necessary and sufficient
condition for stability of ball shape in the first problem when heat source is
radial, but also is essential in deriving the precise value of symmetry
breaking threshold of insulation material in the second problem, which turns
out to be related to isoperimetric constant and in turn implies that ball
shapes are stable in two dimensions.
