Global solvability for differential complexes

• Grant number: 11/52052-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2012
• End date: February 17, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Adalberto Panobianco Bergamasco
• Grantee: Éder Ritis Aragão Costa
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

One of the goals of this project is to study the problem of global solvability in top degree for a differential complex defined by operators of the type L:=d_t-to(t,A)A, where A:D(A)cH-+H is a self-adjoint, positive-definite, linear operator on a Hilbert space H having a continuous inverse, W is a series of non negative powers of A 1 with coefficients in the space of smooth, closedl-forms on a compact connected manifold ? of dimension n and d_t is the exterior derivative on ?. We intend to study the results of [1] about global hypoellipticity at the first level of the complex, and those of [2], about global solvability at the top level, with the purpose of extending the conclusions therein to a broader context and try to apply them to obtain a global version of the (local) theory given in [3], by using scales of fractional powers spaces more general than those considered there. [1] A.P. Bergamasco, P.D. Cordaro, D. Malagutti, P.A.: Globally hypoeliptic systems of vector fields. J. Funct. Anal. 114, n° 2, 267-285(1993) [2] A.P. Bergamasco, P.D. Cordaro, G. Petronilho, Global solvability for certain classes of undetermined systems of vector fields. [3] F. Treves: Concatenations of second-order evolution equations applied to local solvability and hypoellipticity, Communications on Pure and Applied Mathematics 26 (1973), 201-250. (AU)