65 citations · 156 across the 54 of their papers we have counts for
64 papers
The Liouville equation on Riemannian surfaces: the role of volume growth in classification and rigidity results
Giulio Ciraolo, Alberto Farina, Michele Gatti
We study the Liouville equation on a complete, connected, non-compact, boundaryless Riemannian surface with non-negative Ricci curvature. Assuming only some as…
On the anisotropic critical -Laplace equation: classification, decomposition, and stability results
Carlo Alberto Antonini, Giulio Ciraolo, Michele Gatti
We investigate both qualitative and quantitative issues related to the classification of non-negative energy solutions to the anisotropic critical -Laplace equation in $\mathbb{…
On the classification of solutions to a class of -Liouville equations in
Giulio Ciraolo, Pierpaolo Esposito, Xiaoliang Li
Given and , we consider the following weighted Liouville-type equation involving the -Laplacian: \begin{equation*} \left\{ \begin{aligned} -& Δ_N u = |x|^{Nα} e^…
Symmetry and rigidity results for Serrin's overdetermined type problems in weighted Riemannian manifolds
Laura Accornero, Giulio Ciraolo
We study Serrin's overdetermined boundary value problems in bounded domains on weighted Riemannian manifolds. When the closure of the domain is compact, we establish a rigidity res…
Some remarks on patterns for semilinear Neumann problems
Marta Calanchi, Giulio Ciraolo, Francesca Messina
We study semilinear elliptic equations \begin{equation*} \begin{cases} -Δu = f(u) & \text{in } Ω, \\ \partial_νu = 0 & \text{on } \partialΩ, \end{cases} \end{equation*} with homoge…
Rigidity of weighted manifolds via classification results for semilinear equations
Giulio Ciraolo, Alberto Farina, Troy Petitt
We study model semilinear equations on complete and non-compact weighted Riemannian manifolds with non-negative Bakry-Émery Ricci curvature. Our main goal is to classify positive s…