  The optimal insulation of a heat conducting body by a thin film of variable
thickness can be formulated as a nondifferentiable, nonlocal eigenvalue
problem. The discretization and iterative solution for the reliable computation
of corresponding eigenfunctions that determine the optimal layer thickness are
addressed. Corresponding numerical experiments confirm the theoretical
observation that a symmetry breaking occurs for the case of small available
insulation masses and provide insight in the geometry of optimal films. An
experimental shape optimization indicates that convex bodies with one axis of
symmetry have favorable insulation properties.
