20 citations · 45 across the 21 of their papers we have counts for
22 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 . As…
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 \ }Ω\…
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 sm…
Some remarks on singular capillary cones with free boundary
Alberto Pacati, Giorgio Tortone, Bozhidar Velichkov
We study singular minimizing capillary cones with free boundary. We provide a stability criterion Jerison-Savin and use it to prove that a minimizing capillary cone is flat whe…
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 $…
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…
On the dimension of the singular set in optimization problems with measure constraint
Dario Mazzoleni, Giorgio Tortone, Bozhidar Velichkov
In this paper, we prove estimates on the dimension of the singular part of the free boundary for solutions to shape optimization problems with measure constraints. The focus is on…
Higher order boundary Harnack principle via degenerate equations
Susanna Terracini, Giorgio Tortone, Stefano Vita
As a first result we prove higher order Schauder estimates for solutions to singular/degenerate elliptic equations of type: \[ -\mathrm{div}\left(ρ^aA\nabla w\right)=ρ^af+\mathrm{d…
Regularity of the optimal sets for a class of integral shape functionals
Giuseppe Buttazzo, Francesco Paolo Maiale, Dario Mazzoleni +2
We prove {the first} regularity theorem for the free boundary of solutions to shape optimization problems involving integral functionals, for which the energy of a domain is ob…
Liouville theorems and optimal regularity in elliptic equations
Giorgio Tortone
The objective of this paper is to establish a connection between the problem of optimal regularity among solutions to elliptic PDEs with measurable coefficients and the Liouville p…
On the nodal set of solutions to some sublinear equations without homogeneity
Nicola Soave, Giorgio Tortone
We investigate the structure of the nodal set of solutions to an unstable Alt-Phillips type problem \[ -Δu = λ_+(u^+)^{p-1}-λ_-(u^-)^{q-1} \] where , , $λ_- \g…
The boundary Harnack principle on optimal domains
Francesco Paolo Maiale, Giorgio Tortone, Bozhidar Velichkov
We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that beha…
Epsilon-regularity for the solutions of a free boundary system
Francesco Paolo Maiale, Giorgio Tortone, Bozhidar Velichkov
This paper is dedicated to a free boundary system arising in the study of a class of shape optimization problems. The problem involves three variables: two functions and , a…
Regularity of shape optimizers for some spectral fractional problems
Giorgio Tortone
This paper is dedicated to the spectral optimization problem $$ \mathrm{min}\left\{λ_1^s(Ω)+\cdots+λ_m^s(Ω) + Λ\mathcal{L}_n(Ω)\colon Ω\subset D \mbox{ s-quasi-open}\right\} $$ whe…
A vectorial problem with thin free boundary
Daniela De Silva, Giorgio Tortone
We consider the vectorial analogue of the thin free boundary problem introduced in \cite{CRS} as a realization of a nonlocal version of the classical Bernoulli problem. We study op…
The nodal set of solutions to some nonlocal sublinear problems
Giorgio Tortone
We study the nodal set of solutions to equations of the form where , and and $…
Improvement of flatness for vector valued free boundary problems
Daniela De Silva, Giorgio Tortone
For a vectorial Bernoulli-type free boundary problem, with no sign assumption on the components, we prove that flatness of the free boundary implies regularity, as well-k…
Regularity results for segregated configurations involving fractional Laplacian
Giorgio Tortone, Alessandro Zilio
We study the regularity of segregated profiles arising from competition - diffusion models, where the diffusion process is of nonlocal type and is driven by the fractional Laplacia…
On the nodal set of solutions to degenerate or singular elliptic equations with an application to harmonic functions
Yannick Sire, Susanna Terracini, Giorgio Tortone
This work is devoted to the geometric-theoretic analysis of the nodal set of solutions to degenerate or singular equations involving a class of operators including $$ L_a = \mbox{d…
On s-harmonic functions on cones
Susanna Terracini, Giorgio Tortone, Stefano Vita
We deal with non negative functions satisfying \[ \left\{ \begin{array}{ll} (-Δ)^s u_s=0 & \mathrm{in}\quad C, u_s=0 & \mathrm{in}\quad \mathbb{R}^n\setminus C, \end{array}\right.…