7 papers
Rigidity for the Pólya-Szegö inequality under circular rearrangement
F. Cagnetti, G. Domazakis, M. Perugini +1
A Pólya-Szegö inequality for the circular rearrangement is proven, under general assumptions. In addition, sufficient conditions are given, under which all the extremals of the ine…
Minimally singular functions and the rigidity problem for Steiner's perimeter inequality
Matteo Perugini
Let , and let be an open and connected set with finite Lebesgue measure. Among functions of bounded variation in we introduce the class of \emp…
Perimeter inequality under circular and Steiner symmetrisation: geometric characterisation of extremals
Matteo Perugini
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…
A quantitative version of the Gidas-Ni-Nirenberg Theorem
Giulio Ciraolo, Matteo Cozzi, Matteo Perugini +1
A celebrated result by Gidas, Ni & Nirenberg asserts that classical positive solutions to semilinear equations in a ball vanishing at the boundary must be radial and…
Lower semicontinuity for functionals defined on piecewise rigid functions and on
Manuel Friedrich, Matteo Perugini, Francesco Solombrino
In this work, we provide a characterization result for lower semicontinuity of surface energies defined on piecewise rigid functions, i.e., functions which are piecewise affine on…
Rigidity of Steiner's inequality for the anisotropic perimeter
Matteo Perugini
The aim of this work is to study the rigidity problem for Steiner's inequality for the anisotropic perimeter, that is, the situation in which the only extremals of the inequality a…
Rigidity for perimeter inequality under spherical symmetrisation
Filippo Cagnetti, Matteo Perugini, Dominik Stöger
Necessary and sufficient conditions for rigidity of the perimeter inequality under spherical symmetrisation are given. That is, a characterisation for the uniqueness (up to orthogo…