1 citations · 3 across the 6 of their papers we have counts for
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(Quasi-)conformal methods in two-dimensional free boundary problems
Guido De Philippis, Luca Spolaor, Bozhidar Velichkov
In this paper we study the local behavior of solutions to some free boundary problems. We relate the theory of quasi-conformal maps to the regularity of the solutions to nonlinear…
Positive solutions to the sublinear Lane-Emden equation are isolated
Lorenzo Brasco, Guido De Philippis, Giovanni Franzina
We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first …
Regularity of the free boundary for the two-phase Bernoulli problem
Guido De Philippis, Luca Spolaor, Bozhidar Velichkov
We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As…
The sharp quantitative isocapacitary inequality
Guido De Philippis, Michele Marini, Ekaterina Mukoseeva
We prove a sharp quantitative form of the classical isocapacitary inequality. Namely, we show that the difference between the capacity of a set and that of a ball with the same vol…
Regularity of minimizers for a model of charged droplets
Guido De Philippis, Jonas Hirsch, Giulia Vescovo
We investigate properties of minimizers of a variational model describing the shape of charged liquid droplets. The model, proposed by Muratov and Novaga, takes into account the re…
Implicit time discretization for the mean curvature flow of mean convex sets
Guido De Philippis, Tim Laux
In this note we analyze the Almgren-Taylor-Wang scheme for mean curvature flow in the case of mean convex initial conditions. We show that the scheme preserves strict mean convexit…