Qualitative properties of partial differential equations and several complex variables

• Grant number: 12/17217-0
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2012
• End date: October 31, 2014
• 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

The maim purpose of the project is to continue the work undertaking by the grant Auxílio à Pesquisa Jovem Pesquisador 2008/01247-1, in the study of qualitative properties of partial diffe- rential equations, in connexion with harmonic analysis and functions of several complex variables. In particular, in the study of: i) microlocal analysis of solutions of first order non linear PDE's; ii) a priori estimates (compensated compactness) without the lower bound in the classe of Hardy spaces; iii) a priori estimates (compensated compactness) for elliptic systems of complex vector fields; iv) study of a new class of FBI transform to characterize regularity in the class of ultradifferentiable functions, in particular, Gevrey functions. (AU)