The quantitative isoperimetric inequality and related topics | Bulletin of Mathematical Sciences
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We introduce a diffused interface formulation of the Plateau problem, where the Allen--Cahn
energy $\mathcal {AC} _\varepsilon $ is minimized under a volume constraint $ v $ and a …

The first part of the book is devoted to the transport equation for a given vector field,
exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of …

We provide, in the setting of Gauss' capillarity theory, a rigorous derivation of the equilibrium
law for the three dimensional structures known as Plateau borders which arise in" wet" soap …

Necessary and sufficient conditions for rigidity of the perimeter inequality under spherical
symmetrisation are given. That is, a characterisation for the uniqueness (up to orthogonal …

We provide a geometric characterization of rigidity of equality cases in Ehrhard's
symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a …

In the last centuries, partial differential equations have been used to model many physical
problems: the Navier-Stokes and Euler equations in fluid dynamics, the Boltzmann and …

In this paper, we give necessary and sufficient conditions for the rigidity of the perimeter
inequality under Schwarz symmetrization. The term rigidity refers to the situation in which the …

We study the perimeter inequality under circular symmetrisation, and we provide a full
geometric characterisation of equality cases. A careful inspection of the proof shows that a …

We address the double bubble problem for the anisotropic Grushin perimeter P α, α≥ 0, and
the Lebesgue measure in ℝ 2, in the case of two equal volumes. We assume that the contact …