An approximation, in the sense of \(\Gamma \)-convergence and in any dimension \(d\ge 1\), of Griffith-type functionals, with p-growth (\(p>1\)) in the symmetrized gradient, is provided by means of a sequence of non-local integral functionals depending on the average of the symmetrized gradients on small balls.

中文翻译：

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格里菲斯泛函的非局部近似

在\（\ Gamma \）-收敛的意义上以及格里菲斯类型泛函的任何维度\（d \ ge 1 \）的近似，其中p -growth（\（p> 1 \））对称根据小球上对称梯度的平均值，通过一系列非局部积分函数来提供梯度。