English

Approximate Two-Sphere One-Cylinder Inequality in Parabolic Periodic Homogenization

Analysis of PDEs 2022-07-29 v3

Abstract

In this paper, for a family of second-order parabolic equation with rapidly oscillating and time-dependent periodic coefficients, we are interested in an approximate two-sphere one-cylinder inequality for these solutions in parabolic periodic homogenization, which implies an approximate quantitative propagation of smallness. The proof relies on the asymptotic behavior of fundamental solutions and the Lagrange interpolation technique.

Keywords

Cite

@article{arxiv.2005.00989,
  title  = {Approximate Two-Sphere One-Cylinder Inequality in Parabolic Periodic Homogenization},
  author = {Yiping Zhang},
  journal= {arXiv preprint arXiv:2005.00989},
  year   = {2022}
}

Comments

Section 4: extended the approximate two-spher one-cylinder inequality to the parabolic equalition with potential in homogenization