二维 Mumford-Shah 极小化器的端点正则性
偏微分方程分析
2015-07-08 v3
摘要
我们证明了二维 Mumford-Shah 极小化器在连通弧端点处的 -正则性定理。具体而言，我们表明，如果在给定球 中，某 Mumford-Shah 极小化器的跳跃集在 Hausdorff 距离下足够接近 的一条半径，那么在较小的球内，该跳跃集是一条终止于某内部点 的连通弧，并且在直至 处是 的。
引用
@article{arxiv.1502.02299,
title = {Endpoint regularity of $2$d Mumford-Shah minimizers},
author = {Camillo De Lellis and Matteo Focardi},
journal= {arXiv preprint arXiv:1502.02299},
year = {2015}
}
备注
This paper has been withdrawn by the authors due to a sign error in the last equation of system (2.11). In turn, this implies a change of sign of the last equation in the linearized system (3.1) as well. The linear three annuli property for solutions to the new system (3.1) is no longer valid