Strongly elliptic equations with periodic coefficients in two-dimensional space
Li-Ming Yeh · Zeitschrift für Analysis und ihre Anwendungen · 2024
Regularity for strongly elliptic equations with highly oscillatory \varepsilon -periodic coefficients in two-dimensional space is addressed. In each \varepsilon -cell, the diffusion coefficients of the elliptic equations are \omega^{2}\in(1,\infty) in a small disk with radius \frac{\varepsilon\mu}{4}\,(2) of the solutions is not a large number. Case two is that \varepsilon , \mu\, (=\omega^{-1}) are independent in the elliptic equations. The diffusion coefficients of the elliptic equations are \varepsilon -periodic, discontinuous, and L^{1} -bounded. Lipschitz estimate uniformly in \varepsilon , \mu\,(=\omega^{-1}) for the elliptic solutions is obtained.