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arXiv · 2107.14248

Optimal unique continuation for periodic elliptic equations on large scales

Scott Armstrong·Tuomo Kuusi·Charles Smart
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Abstract

We prove a quantitative, large-scale doubling inequality and large-scale three-ellipsoid inequality for solutions of uniformly elliptic equations with periodic coefficients. These estimates are optimal in terms of the minimal length scale on which they are valid, and are at least "almost" optimal in the prefactor constants--up to, at most, an iterated logarithm of the initial doubling ratio.

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Scott Armstrong, Tuomo Kuusi, Charles Smart. 2021-07-29. Optimal unique continuation for periodic elliptic equations on large scales. https://arxiv.org/abs/2107.14248

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