| eBook ISBN: | 978-1-4704-0225-9 |
| Product Code: | MEMO/134/636.E |
| List Price: | $48.00 |
| MAA Member Price: | $43.20 |
| AMS Member Price: | $28.80 |
| eBook ISBN: | 978-1-4704-0225-9 |
| Product Code: | MEMO/134/636.E |
| List Price: | $48.00 |
| MAA Member Price: | $43.20 |
| AMS Member Price: | $28.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 134; 1998; 92 ppMSC: Primary 35; Secondary 34
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.
ReadershipResearch mathematicians interested in smoothness/regularity of solutions of PDE.
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Table of Contents
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Chapters
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1. Statement of the problems and results
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2. Sums of squares of vector fields on $\mathbb {R}^3$
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3. Sums of squares of vector fields on $\mathbb {R}^5$
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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.
Research mathematicians interested in smoothness/regularity of solutions of PDE.
-
Chapters
-
1. Statement of the problems and results
-
2. Sums of squares of vector fields on $\mathbb {R}^3$
-
3. Sums of squares of vector fields on $\mathbb {R}^5$
