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arXiv · 2609.34747

A rigidity result for a global vectorial free boundary problem with a linear datum

Giovanni Siclari·Bozhidar Velichkov
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Abstract

In this paper we completely classify the minimizers of a measure constraint global vectorial free boundary problem with a linear datum. More precisely, we show that there exists a unique minimizer whose coincidence set is an ellipsoid. We are motivated by the connection of the problem with the blow-ups of the vectorial Bernoulli free boundary problem and the obstacle problem.

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Giovanni Siclari, Bozhidar Velichkov. 2026-09-28. A rigidity result for a global vectorial free boundary problem with a linear datum. https://arxiv.org/abs/2609.34747

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