Nonlinear Eigenvalues and Analytic-Hypoellipticity
Ching-Chau Yu
1998年1月 · American Mathematical Society: Memoirs of the American Mathematical Society 第 636 冊 · American Mathematical Soc.
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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.
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