199 citations · 522 across the 42 of their papers we have counts for
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Existence of isoperimetric sets with densities "converging from below" in
Guido De Philippis, Giovanni Franzina, Aldo Pratelli
In this paper, we consider the isoperimetric problem in the space with density. Our result states that, if the density f is l.s.c. and converges to a positive limit…
Dimensional estimates for singular sets in geometric variational problems with free boundaries
Guido De Philippis, Francesco Maggi
We show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are -negligible, where is the ambient spa…
A note on the dimension of the singular set in free interface problems
Guido De Philippis, Alessio Figalli
The aim of this note is to investigate the size of the singular set of a general class of free interface problems. We show porosity of the singular set, obtaining as a corollary th…
Kinetic formulation and uniqueness for scalar conservation laws with discontinuous flux
Graziano Crasta, Virginia De Cicco, Guido De Philippis
We prove a uniqueness result for BV solutions of scalar conservation laws with discontinuous flux in several space dimensions. The proof is based on the notion of kinetic solution…
Regularity of free boundaries in anisotropic capillarity problems and the validity of Young's law
Guido De Philippis, Francesco Maggi
Local volume-constrained minimizers in anisotropic capillarity problems develop free boundaries on the walls of their containers. We prove the regularity of the free boundary outsi…