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

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.

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

References in corpus (3)

• The stability for the Cauchy problem for elliptic equations
• Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates
• A note on unique continuation for discrete harmonic functions

Cited by in corpus (1)

• A Carleman-Type Inequality in Elliptic Periodic Homogenization