Optimal unique continuation for periodic elliptic equations on large scales

2021/07/29 by Scott Armstrong, Tuomo Kuusi, Armstrong, Scott +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2107.14248

20 pages

arxiv created 2021/07/29 · arxiv updated 2021/08/02

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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