70 citations · 151 across the 19 of their papers we have counts for
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math.AP2015★ 8 cited
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…
math.AP2015★ 19 cited
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 $…
math.AP2015
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…