Matteo Rizzi

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20232026

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math.AP2026

The Allen-Cahn equation and general minimal cones

Oscar Ivan Agudelo Rico, Matteo Rizzi

We construct solutions to the Allen-Cahn equation $Δ u + u - u^{3} = 0$ in $R^{N + 1}$ , with $N \geq 3$ , whose zero level set is asymptotic (at infinity) to a given minimal cone. Our c…

math.AP2026

Global boundedness and normalized solutions to a $p$ -Laplacian equation

Raj Narayan Dhara, Matteo Rizzi

In the paper, we prove the existence of radial solutions to \begin{equation}\notag%\label{main-eq-abstarct} %\begin{aligned} -Δ_p u+({\rm sgn}(p-s)+V(x))|u|^{p-2}u+λ|u|^{s-2}u=|u|^…

The Allen-Cahn equation and general minimal cones

Global boundedness and normalized solutions to a p-Laplacian equation

Global boundedness and normalized solutions to a $p$ -Laplacian equation