A new class of Hardy spaces and microlocal analysis of traces of solutions of PDEs

• Grant number: 08/01247-1
• Support Opportunities: Research Grants - Young Investigators Grants
• Start date: September 01, 2008
• End date: August 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Gustavo Hoepfner
• Grantee: Gustavo Hoepfner
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

This project involve areas of PDEs, harmonic analysis and several complex variables. In particular it deals with: i) microlocal regularity of boundary values in involutive structures; ii) microlocal regularity of solutions of first order non-linear PDEs; iii) existence of boundary values (in the sense of ultradistributions) of homogeneous solutions of locally integrable planar vector fields; iv) development of a new class of Hardy spaces and study of its functional properties; v) use of this new class to study regularity of solutions in integrable an/or CR structures. (AU)