Shape optimization problems on metric measure spaces

摘要

We consider shape optimization problems of the form. min{J(Ω): Ω?X, m(Ω)≤c}, where X is a metric measure space and J is a suitable shape functional. We adapt the notions of γ-convergence and weak- γ convergence to this new general abstract setting to prove the existence of an optimal domain. Several examples are pointed out and discussed.