Approximate Two-Sphere One-Cylinder Inequality in Parabolic Periodic Homogenization
Yiping Zhang · SIAM Journal on Mathematical Analysis · 2021
In this paper, for a family of second-order parabolic equations 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.