Abstract
This paper is devoted to establishing the pointwise upper and lower bound 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 are C1,γ, 0<γ<1, weaker than the previous C2,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.
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