Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem

IF 1.2 4区数学 Q1 MATHEMATICS

Interfaces and Free Boundaries Pub Date : 2019-08-04 DOI:10.4171/ifb/452

Maria Colombo, L. Spolaor, B. Velichkov

引用次数: 1

Abstract

We answer a question left open in [Arch. Rat. Mech. Anal. 230 (1) (2018), 125-184] and [Arch. Rat. Mech. Anal. 230 (2) (2018), 783-784], by proving that the blow-up limit of minimizers $u$ of the lower dimensional obstacle problem is unique at generic point of the free-boundary. Moreover we show that at such points the only admissible frequencies are $2m-1+s$ and $2m$, $m\geq 1$.

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对于低维障碍问题，几乎处处存在爆破极限的唯一性

我们回答了一个悬而未决的问题。老鼠。械甲怪。[j] .中国农业科学，2018，(1)，125-184。老鼠。械甲怪。[a] . 230(2)(2018)， 783-784]，通过证明低维障碍问题的最小化器的爆破极限$u$在自由边界的一般点上是唯一的。此外，我们表明，在这些点上，唯一允许的频率是$2m-1+s$和$2m$, $m\geq 1$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Interfaces and Free Boundaries 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Interfaces and Free Boundaries is dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems in all areas where such phenomena are pertinent. The journal aims to be a forum where mathematical analysis, partial differential equations, modelling, scientific computing and the various applications which involve mathematical modelling meet. Submissions should, ideally, emphasize the combination of theory and application.