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}
}