Inserted: 11 oct 2002
Last Updated: 7 jul 2005
Journal: Lecture Notes in Math., 1813, Springer, Berlin
To appear in the Lecture Notes in Mathematics, CIME series, school in Martina Franca (September 2001)
We present here a survey on some shape optimization problems that received particular attention in the last years. In particular, we discuss a class of problems, that we call mass optimization problems, where one wants to find the distribution of a given amount of mass which optimizes a given cost functional. The relation with mass transportation problems will be discussed, and several open problems will be presented.
Keywords: shape optimization, transport problems, Monge-Kantorovich equations