English

Optimal unique continuation for periodic elliptic equations on large scales

Analysis of PDEs 2021-08-02 v1

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.

Keywords

Cite

@article{arxiv.2107.14248,
  title  = {Optimal unique continuation for periodic elliptic equations on large scales},
  author = {Scott Armstrong and Tuomo Kuusi and Charles Smart},
  journal= {arXiv preprint arXiv:2107.14248},
  year   = {2021}
}

Comments

20 pages

R2 v1 2026-06-24T04:39:53.895Z