Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.34747

Authors: Siclari, Giovanni, Velichkov, Bozhidar

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca

Awards: G3924550382, G856286776

OpenAlex ID: W7214757937

Cites: 1

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Related to: 10