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

Yan Li

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arxiv 2203.15515 v1 pith:QERQH7IA submitted 2022-03-29 math.AP

Gradient estimates for elliptic systems from composite materials with closely spaced stiff C^(1,γ) inclusions

Yan Li This is my paper

classification math.AP

keywords gammaestimatescompositedamageellipticgradientlowermaterials

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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 H\"{o}lder continuous coefficients in a narrow region where the upper and lower boundaries is $C^{1,\gamma},$ $0<\gamma<1$, weaker than the previous $C^{2,\gamma}$ 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.

Gradient estimates for elliptic systems from composite materials with closely spaced stiff C^(1,γ) inclusions

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