Estimates on the modulus of expansion for vector fields solving nonlinear equations

Lei Ni

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arXiv · 1107.2351

Estimates on the modulus of expansion for vector fields solving nonlinear equations

Lei Ni

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Abstract

By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Schördinger operator with convex potential, which improves an earlier work of Brascamp-Lieb. We also include alternate proofs to the improved log-concavity estimate, and to the fundamental gap theorem of Andrews-Clutterbuck via the elliptic maximum principle. Some applications of the estimates are also obtained, including a sharp lower bound on the first eigenvalue.

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Lei Ni. 2011-07-12. Estimates on the modulus of expansion for vector fields solving nonlinear equations. https://arxiv.org/abs/1107.2351

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