Shape optimization problems on metric measure spaces

Giuseppe Buttazzo; Bozhidar Velichkov

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arXiv · 1312.3915

Shape optimization problems on metric measure spaces

Giuseppe Buttazzo·Bozhidar Velichkov

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Abstract

We consider shape optimization problems of the form $$\min\big\{J(Ω)\ :\ Ω\subset X,\ m(Ω)\le c\big\},$$ 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.

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Giuseppe Buttazzo, Bozhidar Velichkov. 2013-12-13. Shape optimization problems on metric measure spaces. https://arxiv.org/abs/1312.3915

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