Graph-Compatible Power Concavity in Weakly Coupled Elliptic Systems

Jiahuan Li; Hanpeng Zhou

Graph-Compatible Power Concavity in Weakly Coupled Elliptic Systems

Analysis of PDEs 2026-07-13 v1

Authors: Jiahuan Li , Hanpeng Zhou

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.

Cite

@article{arxiv.2607.11513,
  title  = {Graph-Compatible Power Concavity in Weakly Coupled Elliptic Systems},
  author = {Jiahuan Li and Hanpeng Zhou},
  journal= {arXiv preprint arXiv:2607.11513},
  year   = {2026}
}