8 papers
Weighted Robin eigenvalue problems and nonlinear elliptic equations with general growth in the gradient
Francesco Della Pietra, Giuseppina di Blasio, Giuseppe Riey
We prove an existence result for Robin boundary value problems modeled on \[ \begin{cases} Δu + |\nabla u|^2 + λf(x) = 0 & \text{in } Ω \\ \frac{\partial u}{\partial ν} + βu = 0 &…
Normalised solutions and limit profiles of the defocusing Gross-Pitaevskii-Poisson equation
Riccardo Molle, Vitaly Moroz, Giuseppe Riey
We study normalised solutions of the stationary Gross-Pitaevskii-Poisson (GPP) equation with a defocusing local nonlinear term, $$-Δu+λu+|u|^2u =(I_α*|u|^2)u\quad\text{in $\mathbb…
Concave solutions to Finsler -Laplace type equations
Sunra Mosconi, Giuseppe Riey, Marco Squassina
We prove concavity properties for solutions to anisotropic quasi-linear equations, extending previous results known in the Euclidean case. We focus the attention on nonsmooth aniso…
Anisotropic Kelvin-type transform for a class of anisotropic elliptic operators
Francesco Esposito, Giuseppe Riey, Berardino Sciunzi +1
In this paper we introduce and study a new Kelvin-type transform in the anisotropic setting. In particular, we deal with semilinear and quasilinear anisotropic elliptic problems in…
Normalized solutions to mass supercritical Schrodinger equations with negative potential
Riccardo Molle, Giuseppe Riey, Gianmaria Verzini
We study the existence of positive solutions with prescribed -norm for the Schrödinger equation \[ -Δu-V(x)u+λu=|u|^{p-2}u\qquadλ\in \mathbb{R},\quad u\in H^1(\mathbb{R}^N), \…
Hopf Lemma and regularity results for quasilinear anisotropic elliptic equations
Daniele Castorina, Giuseppe Riey, Berardino Sciunzi
We consider a class of quasi-linear anisotropic elliptic equations, possibly degenerate or singular, which are of interest in several applications such as computer vision and conti…
A regularity result for the p-laplacian near uniform ellipticity
Carlo Mercuri, Giuseppe Riey, Berardino Sciunzi
We consider weak solutions to a class of Dirichlet boundary value problems invloving the -Laplace operator, and prove that the second weak derivatives are in with as…
Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces
Alberto Farina, Luigi Montoro, Giuseppe Riey +1
We consider a quasilinear elliptic equation involving a first order term, under zero Dirichlet boundary condition in half spaces. We prove that any positive solution is monotone in…