Fractional elliptic reaction-diffusion systems with coupled gradient terms and different diffusion
Somia Atmani, Kheireddine Biroud, Maha Daoud, El-Haj Laamri · Complex Variables and Elliptic Equations · 2025
In this work, we study the existence and nonexistence of nonnegative solutions to a class of nonlocal elliptic systems set in a bounded open subset of RN. The diffusion operators are of type ui↦di(−Δ)siui where 1≤i≤2,di∈R, 0<s1≠s2<1, and the gradients of the unknowns act as source terms (see (S) below). Existence results are obtained by proving some fine estimates when data belong to weighted Lebesgue spaces. Those estimates are new and interesting in themselves.