Multiple solutions of the forced double pendulum equation

G. Fournier; M. Willem

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Carleman estimates for a subelliptic operator and unique continuation

Nicola Garofalo, Zhongwei Shen (1994)

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We establish a Carleman type inequality for the subelliptic operator $ℒ = Δ_{z} + | x |^{2} \partial_{t}^{2}$ in $ℝ^{n + 1}$ , $n \geq 2$ , where $z \in ℝ^{n}$ , $t \in ℝ$ . As a consequence, we show that $- ℒ + V$ has the strong unique continuation property at points of the degeneracy manifold ${(0, t) \in ℝ^{n + 1} | t \in ℝ}$ if the potential $V$ is locally in certain $L^{p}$ spaces.

On some orthogonal systems of functions

A. C. Zaanen (1940)

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