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Memoirs of the American Mathematical Society Nonlinear Eigenvalues and Analytic hypoellipticity

Name: Memoirs of the American Mathematical Society Nonlinear Eigenvalues and Analytic hypoellipticity
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Bol Partner Studies the failure of analytic-hypoellipticity (AH) of two partial differential operators. The operators studied in this work 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. 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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Studies the failure of analytic-hypoellipticity (AH) of two partial differential operators. The operators studied in this work 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. 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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