Symmetry results for fractional elliptic systems and related problems

Mostafa Fazly (1) , Yannick Sire (2)

1 University of Alberta
2 I2M - Institut de Mathématiques de Marseille

We study elliptic gradient systems with fractional laplacian operators on the whole space $$ (- \Delta)^\mathbf s \mathbf u =\nabla H (\mathbf u) \ \ \text{in}\ \ \mathbf{R}^n,$$ where $\mathbf u:\mathbf{R}^n\to \mathbf{R}^m$, $H\in C^{2,\gamma}(\mathbf{R}^m)$ for $\gamma > \max(0,1-2\min \left \{s_i \right \})$, $\mathbf s=(s_1,\cdots,s_m)$ for $0

Domaines: Equations aux dérivées partielles [math.AP]; Géométrie différentielle [math.DG]

Mostafa Fazly, Yannick Sire. Symmetry results for fractional elliptic systems and related problems. 2014. ⟨hal-01005327⟩