Uniform bounds for strongly competing systems: the optimal Lipschitz case

Nicola Soave, Alessandro Zilio

For a class of systems of semi-linear elliptic equations, including \[ -Δu_i=f_i(x,u_i) - βu_i\sum_{j\neq i}a_{ij}u_j^p,\qquad i=1,\dots,k, \] for $p=2$ (variational-type interacti…