Calculus of Variations and Geometric Measure Theory

G. Buttazzo - L. De Pascale

Optimal Shapes and Masses, and Optimal Transportation Problems

created on 11 Oct 2002
modified by depascal on 07 Jul 2005


Published Paper

Inserted: 11 oct 2002
Last Updated: 7 jul 2005

Journal: Lecture Notes in Math., 1813, Springer, Berlin
Volume: 1813
Pages: 11-51
Year: 2003

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