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.
Optimal shapes and masses, and optimal transportation problems / BUTTAZZO G; DE PASCALE L.. - STAMPA. - 1813:(2003), pp. 11-52. [10.1007/b12016]
Optimal shapes and masses, and optimal transportation problems
DE PASCALE, LUIGI
2003
Abstract
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.
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