| Autor: |
Briani, L., Buttazzo, G., Prinari, F. |
| Rok vydání: |
2021 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost functionals are of the form $P(\Omega)T^q(\Omega)|\Omega|^{-2q-1/2}$ and the class of admissible domains consists of two-dimensional open sets $\Omega$ satisfying the topological constraints of having a prescribed number $k$ of bounded connected components of the complementary set. A relaxed procedure is needed to have a well-posed problem and we show that when $q<1/2$ an optimal relaxed domain exists. When $q>1/2$ the problem is ill-posed and for $q=1/2$ the explicit value of the infimum is provided in the cases $k=0$ and $k=1$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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