7 papers
Optimal partition and segregation problems driven by torsional rigidity
Gabriele Fioravanti, Nicola Soave, Giorgio Tortone
Spectral optimal partition and segregation problems are deeply connected with harmonic maps, eigenfunctions, and the fine structure of nodal sets for linear elliptic equations. In…
Uniqueness of the blow-up for some Alt-Phillips cones
Matteo Carducci, Giorgio Tortone
We establish uniqueness of blow-ups, with sharp quantitative convergence, for several classes of singular minimizing cones in the Alt-Phillips problem, in the range . A…
Vectorial Bernoulli Problems and Free Boundary Systems
Giorgio Tortone, Bozhidar Velichkov
In this survey we go through some of the recent results about the regularity of vectorial free boundary problems of Bernoulli type and free boundary systems. The aim is to illustra…
A priori Hölder estimates for equations degenerating on nodal sets
Susanna Terracini, Giorgio Tortone, Stefano Vita
We prove a priori Hölder bounds for continuous solutions to degenerate equations with variable coefficients of type $$ \mathrm{div}\left(u^2 A\nabla w\right)=0\quad\mathrm{in \ }΅
A priori regularity estimates for equations degenerating on nodal sets
Susanna Terracini, Giorgio Tortone, Stefano Vita
We prove a priori and a posteriori Hölder bounds and Schauder estimates for continuous solutions of degenerate elliptic equations with variable coefficients of the form…
Smoothness and stability in the Alt-Phillips problem
Matteo Carducci, Giorgio Tortone
We study the one-phase Alt-Phillips free boundary problem, focusing on the case of negative exponents . The goal of this paper is twofold. On the one hand, we prove s…