8 papers
Unstable free boundary problems in optimal control theory: existence and regularity
Lorenzo Ferreri, Idriss Mazari-Fouquer, Raphaël Prunier
We establish the first general regularity result for constrained optimal control problems arising naturally in mathematical physics and mathematical biology. Namely, we prove that…
Fine structure of the two-phase Bernoulli free boundaries in 2D
Lorenzo Ferreri, Luca Spolaor, Bozhidar Velichkov
We prove that the branching set of a solution to a two-dimensional two-phase Bernoulli problem with constant coefficients is locally finite. We do this via a Weierstrass representa…
Unique continuation for nonlinear variational problems
Lorenzo Ferreri, Luca Spolaor, Bozhidar Velichkov
This paper is dedicated to the unique continuation properties of the solutions to nonlinear variational problems. Our analysis covers the case of nonlinear autonomous functionals d…
On the boundary branching set of the one-phase problem
Lorenzo Ferreri, Luca Spolaor, Bozhidar Velichkov
We consider minimizers of the one-phase Bernoulli free boundary problem in domains with analytic fixed boundary. In any dimension , we prove that the branching set at the bounda…
On the fine structure of the solutions to nonlinear thin two-membrane problems in 2D
Lorenzo Ferreri, Luca Spolaor, Bozhidar Velichkov
We prove a structure theorem for the solutions of nonlinear thin two-membrane problems in dimension two. Using the theory of quasi-conformal maps, we show that the difference of th…
A capillarity one-phase Bernoulli free boundary problem
Lorenzo Ferreri, Giorgio Tortone, Bozhidar Velichkov
We consider a one-phase Bernoulli free boundary problem in a container - a smooth open subset of - under the condition that on the fixed boundary th…
Regularity for one-phase Bernoulli problems with discontinuous weights and applications
Lorenzo Ferreri, Bozhidar Velichkov
We study a one-phase Bernoulli free boundary problem with weight function admitting a discontinuity along a smooth jump interface. In any dimension , we show the …
A one-sided two phase Bernoulli free boundary problem
Lorenzo Ferreri, Bozhidar Velichkov
We study a two-phase free boundary problem in which the two-phases satisfy an impenetrability condition. Precisely, we have two ordered positive functions, which are harmonic in th…