Differential and Integral Equations

A note on the dimension of the singular set in free interface problems

Guido De Philippis and Alessio Figalli

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The aim of this note is to investigate the size of the singular set of a general class of free interface problems. We show porosity of the singular set, obtaining as a corollary that both its Hausdorff and Minkowski dimensions are strictly smaller than $n-1$.

Article information

Differential Integral Equations, Volume 28, Number 5/6 (2015), 523-536.

First available in Project Euclid: 30 March 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49Q20: Variational problems in a geometric measure-theoretic setting 35A15: Variational methods


De Philippis, Guido; Figalli, Alessio. A note on the dimension of the singular set in free interface problems. Differential Integral Equations 28 (2015), no. 5/6, 523--536. https://projecteuclid.org/euclid.die/1427744099

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