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Regularity results for almost-minimizers of anisotropic free interface problem with H\"older dependence on the position

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arxiv 2404.02086 v1 pith:HJ7BRD22 submitted 2024-04-02 math.OC

Luca Esposito , Lorenzo Lamberti , Giovanni Pisante This is my paper · ORCID
classification math.OC
keywords almost-minimizersanisotropicbulkenergyinterfaceolderpositionregularity
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We establish regularity results for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surface energy exhibits anisotropic behaviour and is defined by means of an ellipsoidal density that is H\"older continuous with respect to the position variable.

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  1. Quantitative regularity properties for the optimal design problem

    math.OC 2025-05 conditional novelty 7.0 of 10

    An optimal design problem's free boundary is uniformly rectifiable in all dimensions, and in 2D it is fully smooth when β<4α.

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