Higher regularity of the free boundary in the obstacle problem for the fractional heat operator

被引：0
|
作者：
Hu, Xi [1 ]
Tang, Lin [2 ]
机构：
[1] Beijing Normal Univ, Lab Math & Complex Syst, Minist Educ, LMAM,Sch Math Sci, Beijing 100875, Peoples R China
[2] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2024年 / 286卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Boundary Harnack estimate; Extension problem; Fractional heat operator; Free boundary problem; EXTENSION PROBLEM; BEHAVIOR; DOMAINS;
D O I：
10.1016/j.jfa.2023.110274
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a higher regularity result for the free boundary in the obstacle problem for the fractional heat operator via a higher order boundary Harnack estimate. As a consequence, we show that if the obstacle is Hm+beta, then the free boundary is Hm-1+alpha near non-degenerate free boundary points for some 0 < alpha <= beta. In particular, smooth obstacles yield smooth free boundaries near non-degenerate free boundary points.(c) 2023 Elsevier Inc. All rights reserved.
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页数：40
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