Optimal design in conductivity under locally constrained heat-flux
2010 - JC Bellido, A Donoso, P Pedregal
Archive Rational Mechanics and Analysis 195, 333-351 (2010)
This paper addresses the relaxation of an optimal design problem in conductivity under a point-wise constraint on the heat flux. By using a variational approach, developed by the authors in a previous work, we obtained a complete relaxation, involving the explicit computation of constrained quasiconvex envelopes. This relaxed formulation turns out to be very simple in the remarkable compliance case, for which numerical simulations are performed. Those simulations show that our approach and results are interesting from a theoretical point of view as well as from a practical perspective. The emphasis of our work is placed on the local constraint on the heat flux, which seems to be a new ingredient for this kind of optimal design problems.