English

A Carleman-Type Inequality in Elliptic Periodic Homogenization

Analysis of PDEs 2021-02-16 v1

Abstract

In this paper, for a family of second-order elliptic equations with rapidly oscillating periodic coefficients, we are interested in a Carleman-type inequality for these solutions satisfying an additional growth condition in elliptic periodic homogenization, which implies a three-ball inequality without an error term at a macroscopic scale. Moreover, if we replace the additional growth condition by the doubling condition at a macroscopic scale, then the three-ball inequality without an error term holds at any scale. The proof relies on the convergence of H1H^1-norm for the solution and the compactness argument.

Keywords

Cite

@article{arxiv.2102.06891,
  title  = {A Carleman-Type Inequality in Elliptic Periodic Homogenization},
  author = {Yiping Zhang},
  journal= {arXiv preprint arXiv:2102.06891},
  year   = {2021}
}