An invitation to hypoelliptic operators and H\"{o}rmander's vector fields

Hormander's operators are an important class of linear elliptic-parabolic degenerate partial differential operators with smooth coefficients: this text provides the reader with a general overview of the field, with its motivations and problems, some of its fundamental results, and some recent lines [...]
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Hormander's operators are an important class of linear elliptic-parabolic degenerate partial differential operators with smooth coefficients: this text provides the reader with a general overview of the field, with its motivations and problems, some of its fundamental results, and some recent lines of development. These topics have been intensively studied since the late 1960s and are still an active field of research.