Nonelliptic Partial Differential Equations

Analytic Hypoellipticity and the Courage to Localize High Powers of T
Erscheinungsjahr 2013
ISBN: 978-1-4614-2969-2
Verlag: Springer

Buch, Englisch, 203 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 330 g

Reihe: Developments in Mathematics

This book provides a very readable description of a technique, developed by the author years ago but as current as ever, for proving that solutions to certain (non-elliptic) partial differential equations only have real analytic solutions when the data are real analytic (locally). The technique is completely elementary but relies on a construction, a kind of a non-commutative power series, to localize the analysis of high powers of derivatives in the so-called bad direction. It is hoped that this work will permit a far greater audience of researchers to come to a deep understanding of this technique and its power and flexibility.

Zielgruppe

Research

Autoren/Hrsg.

Tartakoff, David S.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

1. What this book is and is not.- 2. Brief Introduction.- 3.Overview of Proofs.- 4. Full Proof for the Heisenberg Group.- 5. Coefficients.- 6. Pseudo-differential Problems.- 7. Sums of Squares and Real Vector Fields.- 8. \bar{\partial}-Neumann and the Boundary Laplacian.- 9. Symmetric Degeneracies.- 10. Details of the Previous Chapter. -11. Non-symplectic Strategem ahe.- 12. Operators of Kohn Type Which Lose Derivatives.- 13. Non-linear Problems.- 14. Treves' Approach.- 15. Appendix.- Bibliography.