Paper detail

Gradient estimates for elliptic systems from composite materials with closely spaced stiff $C^{1,γ}$ inclusions

This paper is devoted to establishing the pointwise upper and lower bounds estimates of the gradient of the solutions to a class of general elliptic systems with Hölder continuous coefficients in a narrow region where the upper and lower boundaries is $C^{1,γ},$ $0<γ<1$, weaker than the previous $C^{2,γ}$ assumption. These estimates play a key role in the damage analysis of composite materials. From our results, the damage may initiate from the narrowest place.