54 citations · 217 across the 31 of their papers we have counts for
46 papers
Density estimates for a (non)local variational model with degenerate double-well potential
Serena Dipierro, Alberto Farina, Giovanni Giacomin +1
In this paper we provide density estimates for a class of functions which includes all the minimizers of the energy $\mathcal{E}_s^p(u,Ω):=(1-s)\left(\frac{1}{2}\int_Ω\int_Ω\frac{|…
Density estimates for a nonlocal variational model with a degenerate double-well potential via the Sobolev inequality
Serena Dipierro, Alberto Farina, Giovanni Giacomin +1
We provide density estimates for level sets of minimizers of the energy $\frac{1}{2} \int_Ω\int_Ω \frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}dxdy+\int_Ω\int_{\mathbb{R}^n\setminusΩ} \frac{|…
Global second-order estimates in anisotropic elliptic problems
Carlo Alberto Antonini, Andrea Cianchi, Giulio Ciraolo +2
We deal with boundary value problems for second-order nonlinear elliptic equations in divergence form, which emerge as Euler-Lagrange equations of integral functionals of the Calcu…
Liouville-type results for some quasilinear anisotropic elliptic equations
Alberto Farina, Berardino Sciunzi, Domenico Vuono
We prove some Liouville-type theorems for stable solutions (and solutions stable outside a compact set) of quasilinear anisotropic elliptic equations. Our results cover the particu…
positivity preservation and Liouville-type theorems
Andrea Bisterzo, Alberto Farina, Stefano Pigola
On a complete Riemannian manifold , we consider distributional solutions of the the differential inequality with a locally bounded func…
Liouville-type theorems for the Lane-Emden equation in the half-space and cones
Louis Dupaigne, Alberto Farina, Troy Petitt
We prove that 0 the only classical solution of the Lane-Emden equation in the half-space which is stable outside a compact set. We also consider weak solutions and the case of gene…