Nonelliptic Partial Differential Equations

Analytic Hypoellipticity and the Courage to Localize High Powers of T

David S. Tartakoff (Autor)

Buch | Softcover

203 Seiten

2013 | 2011 ed.
Springer-Verlag New York Inc.
978-1-4614-2969-2 (ISBN)

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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.

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.

Reihe/Serie	Developments in Mathematics ; 22
Zusatzinfo	VIII, 203 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4614-2969-2 / 1461429692
ISBN-13	978-1-4614-2969-2 / 9781461429692
Zustand	Neuware