Krupchyk, Katsiaryna; Seiler, Werner M.; Tuomela, Jukka Overdetermined elliptic systems. (English) Zbl 1101.35061 Found. Comput. Math. 6, No. 3, 309-351 (2006). The article discusses the notion of ellipticity for overdetermined systems. Naive application of the standard definition leads already to problems, if one considers a first-order form of Laplace’s equations. Traditionally, this is resolved by using an approach based on a weighted symbol leading to the concept of DN-ellipticity (after Douglis and Nirenberg). Here it is shown that a much simpler solution lies in the completion to involution, as the origin of the problem are hidden integrability conditions. More precisely, it is proven that any system that is DN-elliptic becomes elliptic in the standard sense during its completion to involution. The converse is not true, as an explicit counter example demonstrates. Reviewer: Werner M. Seiler (Kassel) Cited in 8 Documents MSC: 35N10 Overdetermined systems of PDEs with variable coefficients 35J45 Systems of elliptic equations, general (MSC2000) Keywords:involution; symbol; DN-ellipticity; hidden integrability conditions Software:SINGULAR PDFBibTeX XMLCite \textit{K. Krupchyk} et al., Found. Comput. Math. 6, No. 3, 309--351 (2006; Zbl 1101.35061) Full Text: DOI