Phase Space Analysis of Partial Differential Equations

Local solvability for operators not of principal type

speaker: Ludovico Pernazza (Università di Pavia)

abstract: The lectures are intended to give an overview of the known results on local solvability for operators of principal type and to show some recent results obtained for operators not of principal type. I will treat Hörmander's theorem on the necessity of condition $(\Psi)$ and Lerner's theorem on the sufficiency of condition $(\Psi)$ in dimension 2 and discuss a new condition $(\Psi^)$ for operators not of principal type leading to new positive and negative results.

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