Regularity Results for an Optimal Design Problem with lower order terms

2021/11/13 by Luca Esposito, Lorenzo Lamberti, Esposito, Luca +1 · 2 citations
Computer Science · Mathematics · Materials Science · #Advanced Mathematical Modeling in Engineering #Mathematical Approximation and Integration #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2111.07197

Abstract

We study the regularity of the interface for optimal energy configurations of functionals involving bulk energies with an additional perimeter penalization of the interface. It is allowed the dependence on (x,u) for the bulk energy. For a minimal configuration (E,u), the Hölder continuity of u is well known. We give an estimate for the singular set of the boundary ∂ E. Namely we show that the Hausdorff dimension of the singular set is strictly smaller than n-1.

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• Ahlfors-regularity for minimizers of a multiphase optimal design problem
• Quantitative regularity properties for the optimal design problem

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