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arXiv · 2207.01369

Spherical Logvinenko-Sereda-Kovrijkine type inequality and null-controllability of the heat equation on the sphere

Alexander Dicke·Ivan Veselic
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Abstract

It is shown that the restriction of a polynomial to a sphere satisfies a Logvinenko-Sereda-Kovrijkine type inequality (a specific type of uncertainty relation). This implies a spectral inequality for the Laplace-Beltrami operator, which, in turn, yields observability and null-controllability with explicit estimates on the control costs for the spherical heat equation that are sharp in the large and in the small time regime.

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Alexander Dicke, Ivan Veselic. 2022-07-04. Spherical Logvinenko-Sereda-Kovrijkine type inequality and null-controllability of the heat equation on the sphere. https://arxiv.org/abs/2207.01369

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