M. Rizzi

activity

20052023

most citedExploring Interacting Topological Insulators with Ultracold Atoms: the Synthetic Creutz-Hubbard Model

156 citations · 2.3k across the 65 of their papers we have counts for

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10 papers · 1 filter

math.AP2021

k-ended $O (m) t im es O (n)$ invariant solutions to the Allen-Cahn equation with infinite Morse index

Oscar Ivan Agudelo Rico, Matteo Rizzi

In this work we study existence, asymptotic behaviour and stability properties of $O (m) t im es O (n)$ invariant solutions of the Allen-Cahn equation $D e l t a u + u (1 - u^{2}) = 0$ in $R^m time…

math.AP2020

Normalized solutions of mass supercritical Schrödinger equations with potential

Thomas Bartsch, Riccardo Molle, Matteo Rizzi +1

This paper is concerned with the existence of normalized solutions of the nonlinear Schrödinger equation \[ -Δu+V(x)u+λu = |u|^{p-2}u \qquad\text{in $R^{N}$ } \] in the mass…

math.AP2019

Doubling construction for $O (m) \times O (n)$ -invariant solutions to the Allen-Cahn equation

Oscar Agudelo, Michal Kowalczyk, Matteo Rizzi

We construct new families of two-ended $O (m) \times O (n)$ -invariant solutions to the Allen- Cahn equation Δu+u-u3=0 in $R^{N + 1}$ , with $N \geq 7$ , whose zero level sets diver…

math.AP2019

Radial and cylindrical symmetry of solutions to the Cahn-Hilliard equation

Matteo Rizzi

The paper is devoted to the classification of entire solutions to the Cahn-Hilliard equation $- Δ u = u - u^{3} - δ$ in $R^{N}$ , with particular interest in those solutions whose nodal set…

math.AP2018

Multiple Delaunay ends solutions of the Cahn-Hilliard equation

Michal Kowalczyk, Matteo Rizzi

Let $Σ$ be a surface of constant mean curvature in $R^{3}$ with multiple Delaunay ends. Assuming that $Σ$ is non degenerate in this paper we construct new solutions to the…

math.AP2017★ 4 cited

Periodic solutions to the Cahn-Hilliard equation in the plane

Andrea Malchiodi, Rainer Mandel, Matteo Rizzi

In this paper we construct entire solutions to the Cahn-Hilliard equation $- Δ (- Δ u + W^{^{'}} (u)) + W^{"} (u) (- Δ u + W^{^{'}} (u)) = 0$ in the Euclidean plane, where $W (u)$ is the standard double-we…

math.AP2017

Positive and nodal single-layered solutions to supercritical elliptic problems above the higher critical exponents

Monica Clapp, Matteo Rizzi

We study the problem% \[ -Δv+λv=| v| ^{p-2}v\text{ in }Ω,\text{\qquad}v=0\text{ on $\partial Ω$ },\text{ }% \] for $λ \in R$ and supercritical exponents $p,$ in domains of the…

math.AP2016

Critical points of a perturbed Otha-Kawasaki functional

Matteo Rizzi

In the paper, we consider a small perturbation of the Otha-Kawasaki functional and we construct at least four critical points close to suitable translations of the Schwarz P surfac…

math.AP2015

Clifford Tori and the singularly perturbed Cahn-Hilliard equation

Matteo Rizzi

In this paper we construct entire solutions $u_{ε}$ to the Cahn-Hilliard equation $- ε^{2} Δ (- ε^{2} Δ u + W^{^{'}} (u)) + W^{"} (u) (- ε^{2} Δ u + W^{^{'}} (u)) = 0$ …

math.AP2014

Symmetry properties of some solutions to some semilinear elliptic equations

Alberto Farina, Andrea Malchiodi, Matteo Rizzi

In this paper we prove some symmetry results for entire solutions to the semilinear equation $- Δ u = f (u)$ , with $f$ nonincreasing in a right neighbourhood of the origin. We consider…

k-ended O(m)timesO(n) invariant solutions to the Allen-Cahn equation with infinite Morse index

Normalized solutions of mass supercritical Schrödinger equations with potential

Doubling construction for O(m)×O(n)-invariant solutions to the Allen-Cahn equation

Radial and cylindrical symmetry of solutions to the Cahn-Hilliard equation

Multiple Delaunay ends solutions of the Cahn-Hilliard equation

Periodic solutions to the Cahn-Hilliard equation in the plane

Positive and nodal single-layered solutions to supercritical elliptic problems above the higher critical exponents

Critical points of a perturbed Otha-Kawasaki functional

Clifford Tori and the singularly perturbed Cahn-Hilliard equation

Symmetry properties of some solutions to some semilinear elliptic equations

k-ended $O (m) t im es O (n)$ invariant solutions to the Allen-Cahn equation with infinite Morse index

Doubling construction for $O (m) \times O (n)$ -invariant solutions to the Allen-Cahn equation