Global hypoellipticity and simultaneous approximability in ultradifferentiable classes

Author(s)

Barostichi, R. F. ; Ferra, I. A. ; Petronilho, G.

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 453, n. 1, p. 104-124, SEP 1 2017.
• Web of Science Citations: 0

Abstract

We start this work by recalling a class of globally hypoelliptic sublaplacians defined on the N-dimensional torus introduced by Himonas and Petronilho and we consider a new class of sublaplacians that generalizes this one and prove that it is globally [omega]-hypoelliptic if and only if the coefficients satisfy a diophantine condition involving a new concept of simultaneous approximability with exponent [omega]. Furthermore we prove that this new class is globally [omega]-hypoelliptic if and only if certain perturbations of its vector fields, by adding more derivatives with respect to other variables, are globally [omega]-hypoelliptic. We also recall the Petronilho's conjecture for the smooth hypoellipticity and present a new class of sublaplacians for which the Petronilho's conjecture holds true in the ultradifferentiable functions setup. (C) 2017 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 12/03168-7 - Geometric theory of PDE and several complex variables
• Grantee: Jorge Guillermo Hounie
• Support Opportunities: Research Projects - Thematic Grants