THE KATO SQUARE ROOT PROBLEM ON AN ARBITRARY DOMAIN OF R d

Julian Bailey (1) , El Maati Ouhabaz (2)

1 MSI, ANU - Mathematics Sciences Institute
2 IMB - Institut de Mathématiques de Bordeaux

We solve the Kato square root problem for elliptic operators with bounded measurable and complex coefficients on any domain. The operators are subject to Dirichlet boundary conditions. WE also allow perturbations by general complex sectorial potentials. Our results hold also for systems.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Julian Bailey, El Maati Ouhabaz. THE KATO SQUARE ROOT PROBLEM ON AN ARBITRARY DOMAIN OF R d. 2019. ⟨hal-02006883⟩