73 citations · 413 across the 37 of their papers we have counts for
5 papers · 2 filters
On stable solutions of boundary reaction-diffusion equations and applications to nonlocal problems with Neumann data
Serena Dipierro, Nicola Soave, Enrico Valdinoci
We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincaré-type inequa…
Multidimensional entire solutions for an elliptic system modelling phase separation
Nicola Soave, Alessandro Zilio
For the system of semilinear elliptic equations \[ ΔV_i = V_i \sum_{j \neq i} V_j^2, \qquad V_i > 0 \qquad \text{in } \] we devise a new method to construct entire so…
Normalized solutions for a system of coupled cubic Schrödinger equations on
Thomas Bartsch, Louis Jeanjean, Nicola Soave
We consider the system of coupled elliptic equations \[ \begin{cases} -Δu - λ_1 u = μ_1 u^3+ βu v^2 \\ -Δv- λ_2 v = μ_2 v^3 +βu^2 v \end{cases} \text{in }, \] and stu…
On phase separation in systems of coupled elliptic equations: asymptotic analysis and geometric aspects
Nicola Soave, Alessandro Zilio
We consider a family of positive solutions to the system of components \[ -Δu_{i,β} = f(x, u_{i,β}) - βu_{i,β} \sum_{j \neq i} a_{ij} u_{j,β}^2 \qquad \text{in }, \] where $…
Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations with nontrivial grouping
Nicola Soave, Hugo Tavares, Susanna Terracini +1
We study regularity issues for systems of elliptic equations of the type \[ -Δu_i=f_{i,β}(x)-β\sum_{j\neq i} a_{ij} u_i |u_i|^{p-1}|u_j|^{p+1} \] set in domains $Ω\subset \mathbb{R…