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arXiv · 1503.02613

Optimal design problems with fractional diffusions

Eduardo V. Teixeira·Rafayel Teymurazyan
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Abstract

In this article we study optimization problems ruled by $\alpha$-fractional diffusion operators with volume constraints. By means of penalization techniques we prove existence of solutions. We also show that every solution is locally of class $C^{0,\alpha}$ (optimal regularity), and that the free boundary is a $C^{1,\gamma}$ surface, up to a $\mathcal{H}^{n-1}$-negligible set.

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Eduardo V. Teixeira, Rafayel Teymurazyan. 2015-03-09. Optimal design problems with fractional diffusions. https://arxiv.org/abs/1503.02613

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