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Nonlinear Eigenvalues and Analytic-Hypoellipticity
Ching-Chau Yu, Federal Home Loan Bank of San Francisco, CA
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Memoirs of the American Mathematical Society
1998; 92 pp; softcover
Volume: 134
ISBN-10: 0-8218-0784-6
ISBN-13: 978-0-8218-0784-2
List Price: US$45
Individual Members: US$27
Institutional Members: US$36
Order Code: MEMO/134/636
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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.

Readership

Research mathematicians interested in smoothness/regularity of solutions of PDE.

Table of Contents

  • 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
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