AI 中文总结
研究平面上Griffith能量几乎极小值函数，通过证明裂纹补集被有限John域覆盖及位移满足估计，推导全梯度可积性与迹线有限性，得出二维中此类函数局部属于SBV^2空间的结论。
AI 中文摘要
我们证明，对于平面上Griffith能量的几乎极小值函数，裂纹的补集局部被有限个John域覆盖，其中位移满足Hölder型估计。由此，我们推导了全梯度的可积性以及沿裂纹迹线的有限性。特别地，我们表明二维中的任何Griffith几乎极小值函数局部属于空间SBV^2。
英文摘要
We show that, for almost-minimizers of the Griffith energy in the plane, the complement of the crack is locally covered by a finite number of John domains where the displacement satisfies Hölder-type estimates. As a consequence, we derive the integrability of the full gradient and the finiteness of the traces along the crack. In particular, we show that any Griffith almost-minimizer in dimension two locally belongs to the space SBV^2.
