In this paper we obtain an interior gradient estimate for a weak solution of a transmission problem with nonsmooth internal boundaries. The coefficients are assumed to be merely measurable in one variable and have small BMO semi-norms in the other variables on each subdomain whose boundary satisfies the so-called delta-Reifenberg flat condition. Under these assumptions, we prove a Calderon-Zygmund type estimate.
Submitted March 24, 2017. Published February 20, 2018.
Math Subject Classifications: 35B65, 35D30, 35J47.
Key Words: Elliptic system; transmission problem; measurable coefficient; Reifenberg domain.
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| Yunsoo Jang |
Center for Mathematical Analysis and Computation (CMAC)
Yonsei University, Seoul 03722, Korea
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