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Memoirs of the American Mathematical Society
1998; 92 pp; softcover
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Order Code: MEMO/134/636
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.
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