Graph-Compatible Power Concavity in Weakly Coupled Elliptic Systems
arXiv:2607.11513
The paper defines graph‑compatible powers for multicomponent weakly coupled elliptic systems based on the coupling graph and proves concavity of the transformed components using a concave‑envelope method and a weighted viscosity comparison principle, also establishing a componentwise constant‑rank theorem that yields strict power concavity under additional assumptions.
Abstract
We introduce graph-compatible powers determined by the coupling graph for multicomponent weakly coupled elliptic systems and establish concavity of the associated transformed components through a concave-envelope method and a weighted viscosity comparison principle. We further establish a componentwise constant-rank theorem for the transformed Hessians, which yields strict power concavity under additional assumptions.