On some recent advances in shape optimization

In this Note we give a short review on recent developements in shape optimization. We explain how the generic non-existence of solutions can be circumvent. Either one can impose some geometric restrictions on the class of admissible domains to get existence (we then explain how to write the usual optimality conditions), or generalized designs are allowed which leads to relaxation by homogenization techniques (we thus obtain topology optimization methods). (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.