English

Denjoy-Carleman Microlocal Regularity on Smooth Real Submanifolds of Complex Space

Analysis of PDEs 2022-07-26 v1

Abstract

We prove the existence of approximate solutions in the (regular) Denjoy-Carleman sense for some systems of smooth complex vector fields. Such approximate solutions provide a well defined notion of Denjoy-Carleman wave front set of distributions on maximally real submanifolds in complex space which can be characterized in terms of the decay of the Fourier-Bros-Iagolnitzer transform. We also apply the approximate solutions to analyze the Denjoy-Carleman microlocal regularity of solutions of certain systems of first-order nonlinear partial differential equations.

Keywords

Cite

@article{arxiv.2207.12017,
  title  = {Denjoy-Carleman Microlocal Regularity on Smooth Real Submanifolds of Complex Space},
  author = {Antonio Victor da Silva and Nicholas Braun Rodrigues},
  journal= {arXiv preprint arXiv:2207.12017},
  year   = {2022}
}