Calculus of Variations and Geometric Measure Theory
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V. Franceschi

A minimal partition problem with trace constraint in the Grushin plane

created by franceschi on 02 Aug 2016
modified on 31 Aug 2017


Published Paper

Inserted: 2 aug 2016
Last Updated: 31 aug 2017

Journal: Calc. Var. Partial Differential Equations
Year: 2017


We study a variational problem for the perimeter associated with the Grushin plane, called minimal partition problem with trace constraint. This consists in studying how to enclose three prescribed areas in the Grushin plane, using the least amount of perimeter, under an additional "one-dimensional" constraint on the intersections of their boundaries. We prove existence of regular solutions for this problem, and we characterize them in terms of isoperimetric sets, showing di fferences with the Euclidean case. The problem arises from the study of quantitative isoperimetric inequalities and has connections with the theory of minimal clusters.


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