Hypoellipticity of rotationally invariant differential forms with a singularity

Author(s)

Fernanda Martins Simão

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2023-03-03

Examining board members

Paulo Leandro Dattori da Silva; Gabriel Cueva Candido Soares de Araujo; Renata de Oliveira Figueira; Alexandre Kirilov

• Advisor: Paulo Leandro Dattori da Silva

Abstract

This dissertation is dedicated to the study of the C∞-hypoellipticity of the class of smooth differential 1-forms that are rotationally invariant, have an irreducible singularity at the origin of R2 and are elliptical outside of it. Consider Ω a differential 1-form under the above conditions and let k+2 and l +2 be the vanishing orders at the origin of the 2-forms Ω Λ Ω and Ω Λ (¯zdz+zd ¯z), respectively. We will present the results of A. Meziani that show that, for k ≥ 2l, under certain assumptions Ω is not C∞-hypoelliptic. For k < 2l, Ω is C∞-hypoelliptic if considered acting on a subspace of 1-forms (AU)

• FAPESP's process: 20/14106-9 - Local solvability of rotationally invariant differential forms
• Grantee: Fernanda Martins Simão
• Support Opportunities: Scholarships in Brazil - Master