Geometric Analysis of PDEs, Propagation of Singularities and solvability

Scientific-Disciplinary Group

01/MATH-03 - Mathematical Analysis, Probability And Mathematical Statistics

Description

The research project deals with the study of propagation of singularity properties for PDEs related to Weyl quantizations of complex quadratic forms, with the aim of studying the global (on the whole Euclidean space) solvability of that class of equations. The objective of the study is obtaining the analogue of the solvability of principal type psedudodifferential operators with complex principal symbol, due to Duistermaat and Hörmander in their celebrated paper Fourier Integral Operators II. The objective is therefore that of obtaining existence of global solutions (with codimension, on the whole Euclidean space) of PDEs of the kind described earlier through a priori estimates that are obtained by means of the propagation of graded singularities and of the graded regularity in Shubin’s Sobolev spaces. This study in the scalar case is then preparatory for that of vector-valued systems by means of isotropic polarized wave-front sets.

Job posting website

https://bandi.unibo.it/ricerca/incarichi-di-ricerca

Funding body

ALMA MATER STUDIORUM - UNIVERSITA' DI BOLOGNA - - DIPARTIMENTO DI MATEMATICA

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