Titlebook: An Invitation to Hypoelliptic Operators and H?rmander‘s Vector Fields; Marco Bramanti Book 2014 The Author(s) 2014 H?rmander‘s operators.H

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https://doi.org/10.1007/978-3-531-19739-5ial geometric tools. The chapter surveys three fundamental papers of the middle 1970’s on this subject, which introduced a number of ideas and techniques which are still part of the indispensable background in this area.

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,H?rmander’s Operators: Why they are Studied,rical” motivations for this field of research, namely Kolmogorov-Fokker-Planck equations arising in the study of stochastic systems, and some relevant PDEs which arise in the theory of several complex variables, in particular the Kohn-Laplacian on the Heisenberg group.

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,A Priori Estimates in Sobolev Spaces for H?rmander’s Operators,ial geometric tools. The chapter surveys three fundamental papers of the middle 1970’s on this subject, which introduced a number of ideas and techniques which are still part of the indispensable background in this area.

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,Geometry of H?rmander’s Vector Fields,induced by a system of vector fields, which are contained in some papers of the middle 1980’s. This area is by a now an independent field of study, but here we are mainly interested in its relevance in connection with the study of second order PDEs of H?rmander’s type.

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2191-8198 ch. 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..978-3-319-02086-0978-3-319-02087-7Series ISSN 2191-8198 Series E-ISSN 2191-8201

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