Electron. J. Differential Equations, Vol. 2018 (2018), No. 52, pp. 1-16.

Gradient estimates for transmission problems with nonsmooth internal boundaries

Yunsoo Jang

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
email: yjang@yonsei.ac.kr

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