This work studies the failure of analytic-hypoellipticity (AH) of two partial differential operators. The operators studied are sums of squares of real analytic vector fields and satisfy Hormander's condition; a condition on the rank of the Lie algebra generated by the brackets of the vector fields. These operators are necessarily $C^\infty$-hypoelliptic. By reducing to an ordinary differential operator, the author shows the existence of nonlinear eigenvalues, which is used to disprove analytic-hypoellipticity of the original operators.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Gewicht
ISBN-13
978-0-8218-0784-2 (9780821807842)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
Statement of the problems and results Sums of squares of vector fields on $\mathbb R^3$ Sums of squares of vector fields on $\mathbb R^5$ Bibliography.
