Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 10, Number 2 (2019), 262-276.
Partial hypoellipticity for a class of abstract differential complexes on Banach space scales
In this article we give sufficient conditions for the hypoellipticity in the first level of the abstract complex generated by the differential operators , , where is a sectorial operator in a Banach space , with , and is a series of nonnegative powers of with coefficients in , being an open set of with arbitrary. Analogous complexes have been studied by several authors in this field, but only in the case and with a Hilbert space. Therefore, in this article, we provide an improvement of these results by treating the question in a more general setup. First, we provide sufficient conditions to get the partial hypoellipticity for that complex in the elliptic region. Second, we study the particular operator , for , which will allow us to solve the problem of points which do not belong to the elliptic region.
Ann. Funct. Anal., Volume 10, Number 2 (2019), 262-276.
Received: 21 February 2018
Accepted: 23 August 2018
First available in Project Euclid: 22 March 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46Fxx: Distributions, generalized functions, distribution spaces [See also 46T30]
Secondary: 47Dxx: Groups and semigroups of linear operators, their generalizations and applications 47Fxx: Partial differential operators [See also 35Pxx, 58Jxx]
Aragão-Costa, E. R. Partial hypoellipticity for a class of abstract differential complexes on Banach space scales. Ann. Funct. Anal. 10 (2019), no. 2, 262--276. doi:10.1215/20088752-2018-0023. https://projecteuclid.org/euclid.afa/1553241620