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Regularity of isoperimetric sets in \(\mathbb R^2\) with density

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Abstract

We consider the isoperimetric problem in \(\mathbb R^2\) with density. We show that, if the density is \(\mathrm{C}^{0,\alpha }\), then the boundary of any isoperimetric set is of class \(\mathrm{C}^{1,\frac{\alpha }{3-2\alpha }}\). This improves the previously known regularity.

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  1. Friedrich-Alexander-Universitat Erlangen-Nurnberg, Erlangen, Germany

    E. Cinti & A. Pratelli

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  1. E. Cinti
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  2. A. Pratelli
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Correspondence to A. Pratelli.

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Cinti, E., Pratelli, A. Regularity of isoperimetric sets in \(\mathbb R^2\) with density. Math. Ann. 368, 419–432 (2017). https://doi.org/10.1007/s00208-016-1409-y

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  • DOI: https://doi.org/10.1007/s00208-016-1409-y

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