Analytic stratifications and the cut locus of a class of distance functions

Albano P; Bove A

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Analytic stratifications and the cut locus of a class of distance functions

机译：一类距离函数的解析分层和割迹

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We study the analytic singularities of viscosity solutions of equations of eikonal type and obtain that the analytic singular support of these functions has an analytic stratification. The singular support can be identified with the cut locus of the distance to the boundary of an open set, when the interior is equipped with a degenerate Riemannian metric. We apply the result to elliptic equations as well as to model operators of Grusin type.

机译：我们研究了eikonal型方程的粘性解的解析奇点，并得到这些函数的解析奇点支持具有解析层次。当内部装有简并的黎曼度量时，可以用到开放集边界的距离的切入轨迹来识别奇异支撑。我们将结果应用于椭圆方程以及Grusin类型的模型算子。

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《Israel Journal of Mathematics》 |2006年第0期|共31页
作者
Albano P; Bove A;
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正文语种 eng
中图分类数学;
关键词
HAMILTON-JACOBI EQUATIONS; VISCOSITY SOLUTIONS; DIFFERENTIAL EQUATIONS; ELLIPTIC OPERATORS; SUBANALYTIC SETS; UNIQUENESS; MANIFOLDS;

机译：HAMILTON-JACOBI方程;粘度解;微分方程;椭圆算子;亚分析集;唯一性;流形;

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1. Analytic stratifications and the cut locus of a class of distance functions [J] . Paolo Albano, Antonio Bove Israel Journal of Mathematics . 2006,第1期

机译：一类距离函数的解析分层和割迹
2. Laplacian of the distance function on the cut locus on a Riemannian manifold [J] . Generau Francois Nonlinearity . 2020,第8期

机译：拉米扬尼亚歧管的距离功能的拉普拉斯
3. THE CUT LOCUS AND DISTANCE FUNCTION FROM A CLOSED SUBSET OF A FINSLER MANIFOLD [J] . Sabau Sorin V., Tanaka Minoru Houston Journal of Mathematics . 2016,第4期

机译：芬斯勒流形的封闭子集的剪切轨迹和距离函数
4. Some Boundary Problems of Theory of Analytic Functions for a Disk with Cuts [C] . GURAM KUTATELADZE WSEAS International Conferences . 2009

机译：截止磁盘分析函数理论的一些边界问题
5. Weighted Composition Operators Acting on Some Classes of Banach Spaces of Analytic Functions [D] . Hmidouch, Nacir. 2017

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6. Turtle Functions Downstream of Cut in Differentially Regulating Class Specific Dendrite Morphogenesis in Drosophila [O] . Mikolaj J. Sulkowski, Srividya Chandramouli Iyer, Mathieu S. Kurosawa, 2011

机译：在果蝇中差异调节类特异树突形态发生的切口的龟功能。
7. The cut locus and distance function from a closed subset of a Finsler manifold [O] . Tanaka, Minoru, Sabau, Sorin V. 2012

机译：切割轨迹和距离函数来自Finsler的闭合子集多种
8. Generic Cut Loci on Surfaces and Their Generic Transformations via Singularity211 Theory for Riemannian Distance Functions [R] . Gershkovich, V., Rubinstein, H. 1998

机译：基于奇点理论的黎曼距离函数表面上的通用切割位置及其一般变换

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Analytic stratifications and the cut locus of a class of distance functions

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