Bechtel, SebastianSebastianBechtelHutcheson, CodyCodyHutchesonSchmatzler, TimotheusTimotheusSchmatzlerTasci, TolgahanTolgahanTasciWittig, MattesMattesWittig2026-04-092026-04-092026-06-01Journal of Evolution Equations 26 (2): 45 (2026)https://hdl.handle.net/11420/62540We obtain the Kato square root property for coupled second-order elliptic systems in divergence form subject to mixed boundary conditions on an open and possibly unbounded set in Rn under two simple geometric conditions: The Dirichlet boundary parts for the respective components are Ahlfors–David regular and a quantitative connectivity property in the spirit of locally uniform domains holds near the remaining Neumann boundary parts. In contrast with earlier work, our proof is not based on the first-order approach due to Axelsson–Keith–McIntosh but uses a second-order approach in the spirit of the original solution to the Kato square root problem on Euclidean space. This way, the proof becomes substantially shorter and technically less demanding.en1424-320220262Springerhttps://creativecommons.org/licenses/by/4.0/Ahlfors–David regular setsKato square root problemLocally uniform domainsSecond-order approachT(b)-argumentNatural Sciences and Mathematics::515: Analysis::515.3: Differential calculus and equationsJournal Articlehttps://doi.org/10.15480/882.1695210.1007/s00028-026-01187-w10.15480/882.16952