The fractional unstable obstacle problem

被引：3

作者：

Allen, Mark ^{[1
]}

Garcia, Mariana Smit Vega ^{[2
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[2] Western Washington Univ, Dept Math, BH 230, Bellingham, WA 98225 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 193卷

关键词：

Obstacle problem; Unstable; Free boundary; EXTENSION PROBLEM;

D O I：

10.1016/j.na.2019.02.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a model for combustion on a boundary. Specifically, we study certain generalized solutions of the equation (-Delta)(u)(s) = chi({u > c}) for 0 < s < 1 and an arbitrary constant c. Our main object of study is the free boundary partial derivative{u > c}. We study the behavior of the free boundary and prove an upper bound for the Hausdorff dimension of the singular set. We also show that when s <= 1/2 certain symmetric solutions are stable; however, when s > 1/2 these solutions are not stable and therefore not minimizers of the corresponding functional. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页数：19

共 8 条

[1]

Allen M., 2013, THESIS

[2] THE TWO-PHASE FRACTIONAL OBSTACLE PROBLEM [J].