Local Hypoellipticity by Lyapunov Function

E. R. Aragão-Costa

Abstract and Applied Analysis, 2016, vol. 2016, 1-8

Abstract:

We treat the local hypoellipticity, in the first degree, for a class of abstract differential operators complexes; the ones are given by the following differential operators: , , where is a self-adjoint linear operator, positive with , in a Hilbert space , and is a series of nonnegative powers of with coefficients in , being an open set of , for any , different from what happens in the work of Hounie (1979) who studies the problem only in the case . We provide sufficient condition to get the local hypoellipticity for that complex in the elliptic region, using a Lyapunov function and the dynamics properties of solutions of the Cauchy problem ′ , , being the first coefficient of . Besides, to get over the problem out of the elliptic region, that is, in the points ∗   such that ∗ = 0, we will use the techniques developed by Bergamasco et al. (1993) for the particular operator .

Date: 2016
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2016/7210540.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2016/7210540.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:7210540

DOI: 10.1155/2016/7210540

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().